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Estimates for differential operators of vector analysis involving $L^{1}$ -norm

Vladimir G. Maz'ya — 2010

Journal of the European Mathematical Society

Приложения некоторых интегральных неравенств к теории квазилинейных эллиптических уравнений

Vladimir G. Maz'ya — 1972

Commentationes Mathematicae Universitatis Carolinae

Об одном операторе вложения и функциях множества типа $(p, l)$ -ёмкости

Vladimir G. Maz'ya — 1973

Commentationes Mathematicae Universitatis Carolinae

On «power-logarithmic» solutions of the Dirichlet problem for elliptic systems in $K_{d} \times R^{n - d}$ , where $K_{d}$ is a d-dimensional cone

Vladimir A. Kozlov; Vladimir G. Maz'ya — 1996

Atti della Accademia Nazionale dei Lincei. Classe di Scienze Fisiche, Matematiche e Naturali. Rendiconti Lincei. Matematica e Applicazioni

A description of all «power-logarithmic» solutions to the homogeneous Dirichlet problem for strongly elliptic systems in a $n$ -dimensional cone $K = K_{d} \times R^{n - d}$ is given, where $K_{d}$ is an arbitrary open cone in $R^{d}$ and $n > d > 1$ .

Gradient regularity via rearrangements for $p$ -Laplacian type elliptic boundary value problems

Andrea Cianchi; Vladimir G. Maz'ya — 2014

Journal of the European Mathematical Society

A sharp estimate for the decreasing rearrangement of the length of the gradient of solutions to a class of nonlinear Dirichlet and Neumann elliptic boundary value problems is established under weak regularity assumptions on the domain. As a consequence, the problem of gradient bounds in norms depending on global integrability properties is reduced to one-dimensional Hardy-type inequalities. Applications to gradient estimates in Lebesgue, Lorentz, Zygmund, and Orlicz spaces are presented.

Продолжение функций из классов С. Л. Соболева во внешность области с вершиной пика на границе II

Vladimir G. Maz'ya; S. V. Poborchij — 1987

Czechoslovak Mathematical Journal

Продолжение функций из классов С. Л. Соболева во внешность области с вершиной пика на границе, I.

Vladimir G. Maz'ya; S. V. Poborchij — 1986

Czechoslovak Mathematical Journal

On pointwise interpolation inequalities for derivatives

Vladimir G. Maz'ya; Tatjana Olegovna Shaposhnikova — 1999

Mathematica Bohemica

Pointwise interpolation inequalities, in particular, ku(x)c(Mu(x)) 1-k/m (Mmu(x))k/m, k<m, and |Izf(x)|c (MIf(x))Re z/Re (Mf(x))1-Re z/Re , 0<Re z<Re<n, where $\nabla_{k}$ is the gradient of order $k$ , $ℳ$ is the Hardy-Littlewood maximal operator, and $I_{z}$ is the Riesz potential of order $z$ , are proved. Applications to the theory of multipliers in pairs of Sobolev spaces are given. In particular, the maximal algebra in the multiplier space $M (W_{p}^{m} (ℝ^{n}) \to W_{p}^{l} (ℝ^{n}))$ is described.

Water-wave problem for a vertical shell

Nikolai G. Kuznecov; Vladimir G. Maz'ya — 2001

Mathematica Bohemica

The uniqueness theorem is proved for the linearized problem describing radiation and scattering of time-harmonic water waves by a vertical shell having an arbitrary horizontal cross-section. The uniqueness holds for all frequencies, and various locations of the shell are possible: surface-piercing, totally immersed and bottom-standing. A version of integral equation technique is outlined for finding a solution.

Boundary integral equations of elasticity in domains with piecewise smooth boundaries

Maz'ya, Vladimir G. — 1986

Equadiff 6

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