EUDML

Currently displaying 1 – 16 of 16

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Solvability and asymptotic behavior of solutions of ordinary differential equations with variable operator coefficients

Vladimir Kozlov; Vladimir Maz'ya — 1992

Journées équations aux dérivées partielles

Boundary singularities of solutions to quasilinear elliptic equations

Vladimir Kozlov; Vladimir Maz'ya — 1999

Journées équations aux dérivées partielles

Asymptotic formulae for solutions to boundary value problems for linear and quasilinear elliptic equations and systems near a boundary point are discussed. The boundary is not necessarily smooth. The main ingredient of the proof is a spectral splitting and reduction of the original problem to a finite-dimensional dynamical system. The linear version of the corresponding abstract asymptotic theory is presented in our new book “Differential equations with operator coefficients”, Springer, 1999.

Asymptotic formula for solutions to the Dirichlet problem for elliptic equations with discontinuous coefficients near the boundary

Vladimir Kozlov; Vladimir Maz'ya — 2003

Annali della Scuola Normale Superiore di Pisa - Classe di Scienze

We derive an asymptotic formula of a new type for variational solutions of the Dirichlet problem for elliptic equations of arbitrary order. The only a priori assumption on the coefficients of the principal part of the equation is the smallness of the local oscillation near the point.

The form boundedness criterion for the relativistic Schrödinger operator

Vladimir Maz'ya; Igor Verbitsky — 2004

Annales de l’institut Fourier

We establish necessary and sufficient conditions on the real- or complex-valued potential $Q$ defined on $ℝ^{n}$ for the relativistic Schrödinger operator $\sqrt{- Δ} + Q$ to be bounded as an operator from the Sobolev space $W_{2}^{1 / 2} (ℝ^{n})$ to its dual $W_{2}^{- 1 / 2} (ℝ^{n})$ .

On Wiener's type regularity of a boundary point for higher order elliptic equations

Maz'ya, Vladimir — 1999

Nonlinear Analysis, Function Spaces and Applications

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

Boundary integral equations of elasticity in domains with piecewise smooth boundaries

Maz'ya, Vladimir G. — 1986

Equadiff 6

Asymptotic analysis of surface waves due to high-frequency disturbances

Nikolay Kuznetsov; Vladimir Gilelevich Maz'ya — 1997

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

The present paper is devoted to the asymptotic analysis of the linear unsteady surface waves. We study two problems concerned with high-frequency surface and submerged disturbances. The two-scale asymptotic series are obtained for the velocity potential. The principal terms in the asymptotics of some hydrodynamical characteristics of the wave motion (the free surface elevation, the energy, etc.) are described.

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