Publications
2015
Boundedness of the gradient of a solution and Wiener test of order one for the biharmonic equation
Mayboroda, S., & Maz'ya, V. (2015). Boundedness of the gradient of a solution and Wiener test of order one for the biharmonic equation. Retrieved from http://arxiv.org/abs/1508.04492v1
2010
Differentiability of Solutions to Second-Order Elliptic Equations via Dynamical Systems
Maz'ya, V., & McOwen, R. (2010). Differentiability of Solutions to Second-Order Elliptic Equations via Dynamical Systems. Retrieved from http://arxiv.org/abs/1004.1618v2
Asymptotic treatment of perforated domains without homogenization
Maz'ya, V., & Movchan, A. (2010). Asymptotic treatment of perforated domains without homogenization. Math. Nachr., 283(1), 104-125.
Boundary integral equations on contours with peaks
Maz'ya, V. G., & Soloviev, A. A. (2010). Boundary integral equations on contours with peaks. Basel: Birkhauser Verlag, Springer.
Elliptic equations in polyhedral domains
Mazya, V., & Rossmann, J. (2010). Elliptic equations in polyhedral domains. Providence: Mathematical Surveys and Monographs, 162..
Green kernels for transmission problems in bodies with small inclusions, Operator Theory and its Applications. In memory of V.B. Lidsky (1924-2008)
Maz'ya, V., Movchan, A., & Nieves, M. (2010). Green kernels for transmission problems in bodies with small inclusions, Operator Theory and its Applications. In memory of V.B. Lidsky (1924-2008). Amer. Math. Soc. Transl., 231(2), 127-160.
On solvability of boundary integral equations of potential theory for a multidimentional cusp domain
Maz'ya, V., & Poborchii, S. (2010). On solvability of boundary integral equations of potential theory for a multidimentional cusp domain. Journal of Mathematical Sciences,, 164(3), 403-414.
On the fundamental solution of an elliptic equation in nondivergence form, Nonlinear Partial Differential Equations and Related Topics
Mazya, V., & McOwen, R. (2010). On the fundamental solution of an elliptic equation in nondivergence form, Nonlinear Partial Differential Equations and Related Topics. Amer. Math. Soc. Transl., 229(2), 145-172.
2009
A quasi-commutativity property of the Poisson and composition operators
Cialdea, A., & Maz'ya, V. (2009). A quasi-commutativity property of the Poisson and composition operators. Retrieved from http://arxiv.org/abs/0910.5750v1
Optimal estimates for the gradient of harmonic functions in the multidimensional half-space
Kresin, G., & Maz'ya, V. (2009). Optimal estimates for the gradient of harmonic functions in the multidimensional half-space. Retrieved from http://arxiv.org/abs/0909.1932v1
Well-posed elliptic Neumann problems involving irregular data and domains
Alvino, A., Cianchi, A., Maz'ya, V., & Mercaldo, A. (2009). Well-posed elliptic Neumann problems involving irregular data and domains. Retrieved from http://dx.doi.org/10.1016/j.anihpc.2010.01.010
Pathological solutions to elliptic problems in divergence form with continuous coefficients
Jin, T., Maz'ya, V., & Schaftingen, J. V. (2009). Pathological solutions to elliptic problems in divergence form with continuous coefficients. C. R. Math. Acad. Sci. Paris 347 (2009), no. 13-14, 773-778. Retrieved from http://dx.doi.org/10.1016/j.crma.2009.05.008
Wiener Type Regularity of a Boundary Point for the 3D Lamé System
Luo, G., & Maz'ya, V. G. (2009). Wiener Type Regularity of a Boundary Point for the 3D Lamé System. Potential Anal. 32 (2), pp. 133--151, 2010. Retrieved from http://arxiv.org/abs/0901.3186v1
On representation of the solution of the Neumann problem in a domain with peak by the harmonic simple layer potential
Maz'ya, V., & Poborchii, S. (2009). On representation of the solution of the Neumann problem in a domain with peak by the harmonic simple layer potential. Vestnik St. Petersburg Univ. Math., 42(3), 185-193.
On the boundedness of first derivatives for solutions to the Neumann-Laplace problem in a convex domain
Maz'ya, V. G. (2009). On the boundedness of first derivatives for solutions to the Neumann-Laplace problem in a convex domain. Unknown Journal, 159(1), 104-112.
The nonhomogeneous Dirichlet problem for the Stokes system in Lipschitz domains with unit normal close to VMO
Maz'ya, V., Mitrea, M., & Shaposhnikova, T. (2009). The nonhomogeneous Dirichlet problem for the Stokes system in Lipschitz domains with unit normal close to VMO. Funct. Anal. Appl., 43(3), 217-235.
Theory of Sobolev Multipliers with Applications to Differential and Integral Operators
Maz'ya, V., & Shaposhnikova, T. (2009). Theory of Sobolev Multipliers with Applications to Differential and Integral Operators (Vol. 337). Berlin: Springer.
Uniform asymptotics of Green's kernels for mixed and Neumann problems in domains with small holes and inclusions
Maz'ya, V., & Movchan, A. (2009). Uniform asymptotics of Green's kernels for mixed and Neumann problems in domains with small holes and inclusions. Sobolev Spaces in Mathematics. III, Int. Math. Ser. (N. Y.), Springer, New York,, 10, 277-316.
Unique solvability of the integral equation for harmonic simple layer potential on the boundary of a domain with a peak
Maz'ya, V., & Poborchii, S. (2009). Unique solvability of the integral equation for harmonic simple layer potential on the boundary of a domain with a peak. Unknown Journal, 42(2), 120-129.
Uniqueness of the solution of an inverse problem of thermoelasticity
Kozlov, V. A., Maz'ya, V. G., & Fomin, A. V. (2009). Uniqueness of the solution of an inverse problem of thermoelasticity. Zh. Vychisl. Mat. Mat. Fiz. (Russian), 49(3), 542-548.
2008
Uniform asymptotic approximations of Green's functions in a long rod
Maz'ya, V., & Movchan, A. (2008). Uniform asymptotic approximations of Green's functions in a long rod. Mathematical Methods in the Applied Sciences, 31(17), 2055-2068. doi:10.1002/mma.1006
Boundedness of the gradient of a solution to the Neumann-Laplace problem in a convex domain
Maz'ya, V. (2008). Boundedness of the gradient of a solution to the Neumann-Laplace problem in a convex domain. Retrieved from http://arxiv.org/abs/0809.2514v2
Integral and isocapacitary inequalities
Maz'ya, V. (2008). Integral and isocapacitary inequalities. Retrieved from http://arxiv.org/abs/0809.2511v1
Estimates for differential operators of vector analysis involving $L^1$-norm
Maz'ya, V. (2008). Estimates for differential operators of vector analysis involving $L^1$-norm. Retrieved from http://arxiv.org/abs/0808.0414v2
Approximate Hermite quasi-interpolation
Lanzara, F., Maz'ya, V., & Schmidt, G. (2008). Approximate Hermite quasi-interpolation. Retrieved from http://arxiv.org/abs/0806.2546v1
Conductor inequalities and criteria for Sobolev-Lorentz two-weight inequalities
Costea, S., & Maz'ya, V. (2008). Conductor inequalities and criteria for Sobolev-Lorentz two-weight inequalities. Retrieved from http://arxiv.org/abs/0804.3051v1
A collection of sharp dilation invariant inequalities for differentiable functions
Maz'ya, V., & Shaposhnikova, T. (2008). A collection of sharp dilation invariant inequalities for differentiable functions. Retrieved from http://arxiv.org/abs/0802.3209v2
A Collection of sharp dilation invariant integral inequalities for differentiable functions
Maz'ya, V., & Shaposhnikova, T. (2008). A Collection of sharp dilation invariant integral inequalities for differentiable functions. Sobolev Spaces in Mathematics I. Sobolev Type Inequalities, 223-248.
Approximate approximations with data on a perturbed uniform grid.
Lanzara, F., Maz'ya, V., & Schmidt, G. (2008). Approximate approximations with data on a perturbed uniform grid.. Z. Anal. Anwend., 27(3), 323-338.
Boundedness of the gradient of a solution and Wiener test of order one for the biharmonic equation
Mayboroda, S., & Maz'ya, V. (2008). Boundedness of the gradient of a solution and Wiener test of order one for the biharmonic equation. Invent. Math., 175(no. 2), 287-334.
Conductor inequalities and criteria for Sobolev-Lorentz two-weight inequalities
Costea, S., & Maz'ya, V. (2008). Conductor inequalities and criteria for Sobolev-Lorentz two-weight inequalities. Sobolev Spaces in Mathematics II. Applications in Analysis and Partial Differential Equations, 103-122.
Essential norms and localization moduli of Sobolev embeddings for general domains.
Lang, J., & Maz'ya, V. (2008). Essential norms and localization moduli of Sobolev embeddings for general domains.. J. Lond. Math. Soc. (2), 78(2), 373-391.
Jacques Hadamard, Legend of Mathematics
Maz'ya, V., & Shaposhnikova, T. (2008). Jacques Hadamard, Legend of Mathematics. Moscow: MCNMO Publishers.
Mixed boundary value problems for the stationary Navier-Stokes System in polyhedral domains
Maz'ya, V., & Rossmann, J. (2008). Mixed boundary value problems for the stationary Navier-Stokes System in polyhedral domains. Arch. Rational Mech. Anal..
Neumann problems and isocapacitary inequalities
Cianchi, A., & Maz'ya, V. (2008). Neumann problems and isocapacitary inequalities. J. Math. Pures Appl. (9), 89(1), 71-105.
On the solvability of the Neumann problem for a planar domain with a peak.
Maz'ya, V. G., & Poborchii, S. V. (2008). On the solvability of the Neumann problem for a planar domain with a peak.. Vestnik St. Petersburg Univ. Math., 41(2), 145-160.
On the solvability of the Neumann problem in a domain with a cusp. (Russian)
Mazʹya, V. G., & PoborchiÄ, S. V. (2008). On the solvability of the Neumann problem in a domain with a cusp. (Russian). Algebra i Analiz, 20(5), 104-154.
Sobolev Spaces in Mathematics, I.
Maz'ya, V. (Ed.) (2008). Sobolev Spaces in Mathematics, I.. New York: Springer and T. Rozhkovskaya.
Sobolev Spaces in Mathematics, II.
Maz'ya, V. (Ed.) (2008). Sobolev Spaces in Mathematics, II.. New York: Springer and T. Rozhkovskaya.
Theory of Sobolev Multipliers with Applications to Differential and Integral Operators
Maz'ya, V., & Shaposhnikova, T. (2008). Theory of Sobolev Multipliers with Applications to Differential and Integral Operators (Vol. 337). Berlin: Springer.
Uniform asymptotic formulae for Green's tensors inelastic singularly perturbed domains with multiple inclusions
Maz'ya, V., Movchan, A., & Nieves, M. (2008). Uniform asymptotic formulae for Green's tensors inelastic singularly perturbed domains with multiple inclusions. Rendiconti Accademia Nazionale delle Scienze detta dei XL, Memorie di Matematica e Applicazioni, 124, X(no. 1), 103-158.
Uniform asymptotics of Green's kernels for mixed and Neumann problems in domains with small holes and inclusions
Maz'ya, V., & Movchan, A. (2008). Uniform asymptotics of Green's kernels for mixed and Neumann problems in domains with small holes and inclusions. Sobolev Spaces in Mathematics III. Applications in Mathematical Physics, 277-316.
2007
Sharp Hardy-Leray inequality for axisymmetric divergence-free fields
Costin, O., & Maz'ya, V. (2007). Sharp Hardy-Leray inequality for axisymmetric divergence-free fields. Retrieved from http://arxiv.org/abs/math/0703116v2
Analytic criteria in the qualitative spectral analysis of the Schroedinger operator
Maz'ya, V. (2007). Analytic criteria in the qualitative spectral analysis of the Schroedinger operator. Retrieved from http://arxiv.org/abs/math/0702427v1
The Dirichlet problem in Lipschitz domains for higher order elliptic systems with rough coefficients
Maz'ya, V., Mitrea, M., & Shaposhnikova, T. (2007). The Dirichlet problem in Lipschitz domains for higher order elliptic systems with rough coefficients. Retrieved from http://arxiv.org/abs/math/0701898v1
A maximum modulus estimate for solutions of the Navier-Stokes system in domains of polyhedral type
Maz'ya, V., & Rossmann, J. (2007). A maximum modulus estimate for solutions of the Navier-Stokes system in domains of polyhedral type. Retrieved from http://arxiv.org/abs/math-ph/0701020v3
$L\sb p$ estimates of solutions to mixed boundary value problems for the Stokes system in polyhedral domains
Maz'ya, V., & Rossmann, J. (2007). $L\sb p$ estimates of solutions to mixed boundary value problems for the Stokes system in polyhedral domains. Math. Nachr., 280(7), 751-793.
A new type of integral equations related to the co-area formula (reduction of dimension in multi-dimensional integral equations)
Maz'ya, V. (2007). A new type of integral equations related to the co-area formula (reduction of dimension in multi-dimensional integral equations). J. Funct. Anal., 245(2), 493-504.
Approximate approximations
Maz'ya, V., & Schmidt, G. (2007). Approximate approximations. Providence, RI: American Mathematical Society.
Bourgain-Brezis type inequality with explicit constants
Maz'ya, V. (2007). Bourgain-Brezis type inequality with explicit constants. Contemporary Mathematics, 445, 247-264.
Embedding and extension theorems for functions in non-Lipschitz domains (Russian)
Maz'ya, V., & Poborchi, S. (2007). Embedding and extension theorems for functions in non-Lipschitz domains (Russian). St. Petersburg: St. Petersburg Publishers, Russia.
Neumann's problems and isocapacitary inequalities
Cianchi, A., & Maz'ya, V. (2007). Neumann's problems and isocapacitary inequalities. J. Math. Pures et Appl., 89, 71-105.
On solvability of the Neumann problem in an energy space for a domain with a peak
Maz'ya, V. G., & Poborchi, S. V. (2007). On solvability of the Neumann problem in an energy space for a domain with a peak. Georgian Math. J., 14(3), 499-518.
Potentials of Gaussians and approximate wavelets
Maz'ya, V., & Schmidt, G. (2007). Potentials of Gaussians and approximate wavelets. Math. Nachr., 280(no. 9-), 1176-1189.
Sharp Bohr type real part estimates
Kresin, G., & Maz'ya, V. (2007). Sharp Bohr type real part estimates. Comput. Methods Funct. Theory, 7(1), 151-165.
Sharp real-part theorems. A unified approach.
Gershon, K., & Vladimir, M. (2007). Sharp real-part theorems. A unified approach. (Vol. 1903). Berlin: Springer.
Uniform asymptotic formulae for Green's tensors in elastic singularly perturbed domains
Maz'ya, V. G., Movchan, A. B., & Nieves, M. J. (2007). Uniform asymptotic formulae for Green's tensors in elastic singularly perturbed domains. Asymptot. Anal., 52(3/4), 173-206.
Weighted positivity of second order elliptic systems
Luo, G., & Maz'ya, V. G. (2007). Weighted positivity of second order elliptic systems. Potential Anal., 27(3), 252-270.
2006
Critical Hardy--Sobolev Inequalities
Filippas, S., Maz'ya, V., & Tertikas, A. (2006). Critical Hardy--Sobolev Inequalities. Retrieved from http://arxiv.org/abs/math/0611484v1
Asymptotics for solutions of elliptic equations in double divergence form
Maz'ya, V., & McOwen, R. (2006). Asymptotics for solutions of elliptic equations in double divergence form. Retrieved from http://arxiv.org/abs/math/0602558v2
Mixed boundary value problems for the Navier-Stokes system in polyhedral domains
Maz'ya, V. G., & Rossmann, J. (2006). Mixed boundary value problems for the Navier-Stokes system in polyhedral domains. Retrieved from http://arxiv.org/abs/math-ph/0602054v1
Criteria for the $L^{p}$-dissipativity of systems of second order differential equations
Cialdea, A., & Maz'ya, V. (2006). Criteria for the $L^{p}$-dissipativity of systems of second order differential equations. Retrieved from http://arxiv.org/abs/math/0602382v1
Uniform asymptotic formulae for Green's kernels in regularly and singularly perturbed domains
Maz'ya, V., & Movchan, A. B. (2006). Uniform asymptotic formulae for Green's kernels in regularly and singularly perturbed domains. Retrieved from http://arxiv.org/abs/math/0601753v3
Uniform asymptotic formulae for Green's functions in singularly perturbed domains
Maz'ya, V., & Movchan, A. (2006). Uniform asymptotic formulae for Green's functions in singularly perturbed domains. Retrieved from http://arxiv.org/abs/math/0601707v2
Gauge optimization and spectral properties of magnetic Schrödinger operators
Kondratiev, V., Maz'ya, V., & Shubin, M. (2006). Gauge optimization and spectral properties of magnetic Schrödinger operators. Retrieved from http://arxiv.org/abs/math/0601057v1
Conductor inequalities and criteria for Sobolev type two-weight imbeddings
Maz'ya, V. (2006). Conductor inequalities and criteria for Sobolev type two-weight imbeddings. J. Comput. Appl. Math, 194(no. 1), 94-114.
On a question of Brezis and Marcus
Filippas, S., Maz'ya, V., & Tertikas, A. (2006). On a question of Brezis and Marcus. Calc. Var. Partial Differential Equations, 25(no. 4), 491-501.
Schauder estimates for solutions to a mixed boundary value problem for the Stokes system in polyhedral domains.
Maz'ya, V. G., & Rossmann, J. (2006). Schauder estimates for solutions to a mixed boundary value problem for the Stokes system in polyhedral domains.. Math. Methods Appl. Sci., 29(no. 9), 965-1017.
Theorems for embedding Sobolev spaces on domains with a peak and on Hölder domains
Maz'ya, V. G., & Poborchi, S. V. (2006). Theorems for embedding Sobolev spaces on domains with a peak and on Hölder domains. Algebra i Analiz, 18(no. 4), 95-126.
2005
Approximate Approximations from scattered data
Lanzara, F., Maz'ya, V., & Schmidt, G. (2005). Approximate Approximations from scattered data. Retrieved from http://arxiv.org/abs/math/0508241v1
Can one see the fundamental frequency of a drum?
Maz'ya, V., & Shubin, M. (2005). Can one see the fundamental frequency of a drum?. Retrieved from http://dx.doi.org/10.1007/s11005-005-0010-1
Asymptotic formula for solutions to elliptic
Kozlov, V., & Maz'ya, V. (2005). Asymptotic formula for solutions to elliptic. Ann. Mat. Pura ed Appl., 184(2), 185-213.
Conductor and capacitary inequalities for functions on topological spaces and their applications
Maz'ya, V. (2005). Conductor and capacitary inequalities for functions on topological spaces and their applications. Journal of Functional Analysis, 224(2), 408-430.
Higher regularity in the classical layer potential theory for Lipschitz domains
Maz'ya, V., & Shaposhnikova, T. (2005). Higher regularity in the classical layer potential theory for Lipschitz domains. Indiana University mathematics Journal, 54(1), 99-142.
Jacques Hadamard, un Math\'ematicien Universel
Maz'ya, V., & Shaposhnikova, T. (2005). Jacques Hadamard, un Math\'ematicien Universel. Paris: EDP Sciences.
Traces of multipliers in pairs of weighted Sobolev spaces
Maz'ya, V., & Shaposhnikova, T. (2005). Traces of multipliers in pairs of weighted Sobolev spaces. Journal of Function Spaces and Applications, 3, 91-115.
2004
Criterion for the $L^{p}$-dissipativity of second order differential operators with complex coefficients
Cialdea, A., & Maz'ya, V. (2004). Criterion for the $L^{p}$-dissipativity of second order differential operators with complex coefficients. Retrieved from http://arxiv.org/abs/math/0412225v1
Form boundedness of the general second order differential operator
Maz'ya, V. G., & Verbitsky, I. E. (2004). Form boundedness of the general second order differential operator. Retrieved from http://arxiv.org/abs/math/0411216v1
Infinitesimal form boundedness and Trudinger's subordination for the Schrödinger operator
Maz'ya, V. G., & Verbitsky, I. E. (2004). Infinitesimal form boundedness and Trudinger's subordination for the Schrödinger operator. Invent. Math. 162 (2005), 81 - 136. Retrieved from http://dx.doi.org/10.1007/s00222-005-0439-y
2003
Discreteness of spectrum and positivity criteria for Schrödinger operators
Maz'ya, V., & Shubin, M. (2003). Discreteness of spectrum and positivity criteria for Schrödinger operators. Annals of Mathematics, 1(2), 919-942. Retrieved from http://arxiv.org/abs/math/0305278v3