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Around the Research of Vladimir Maz'ya II: Partial Differential Equations

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International Mathematical Series Volume 12
Around the Research of Vladimir Maz'ya II
Partial Differential Equations
Edited by Ari Laptev

Numerous influential contributions of Vladimir Maz'ya to PDEs are related to diverse areas. In particular, the following topics, close to the scientific interests of V. Maz'ya are discussed: semilinear elliptic equation with an exponential nonlinearity resolvents, eigenvalues, and eigenfunctions of elliptic operators in perturbed domains, homogenization, asymptotics for the Laplace-Dirichlet equation in a perturbed polygonal domain, the Navier-Stokes equation on Lipschitz domains in Riemannian manifolds, nondegenerate quasilinear subelliptic equations of p-Laplacian type, singular perturbations of elliptic systems, elliptic inequalities on Riemannian manifolds, polynomial solutions to the Dirichlet problem, the first Neumann eigenvalues for a conformal class of Riemannian metrics, the boundary regularity for quasilinear equations, the problem on a steady flow over a two-dimensional obstacle, the well posedness and asymptotics for the Stokes equation, integral equations for harmonic single layer potential in domains with cusps, the Stokes equations in a convex polyhedron, periodic scattering problems, the Neumann problem for 4th order differential operators.

Contributors include: Catherine Bandle (Switzerland), Vitaly Moroz (UK), and Wolfgang Reichel (Germany); Gerassimos Barbatis (Greece), Victor I. Burenkov (Italy), and Pier Domenico Lamberti (Italy); Grigori Chechkin (Russia); Monique Dauge (France), Sebastien Tordeux (France), and Gregory Vial (France); Martin Dindos (UK); Andras Domokos (USA) and Juan J. Manfredi (USA); Yuri V. Egorov (France), Nicolas Meunier (France), and Evariste Sanchez-Palencia (France); Alexander Grigor'yan (Germany) and Vladimir A. Kondratiev (Russia); Dmitry Khavinson (USA) and Nikos Stylianopoulos (Cyprus); Gerasim Kokarev (UK) and Nikolai Nadirashvili (France); Vitali Liskevich (UK) and Igor I. Skrypnik (Ukraine); Oleg Motygin (Russia) and Nikolay Kuznetsov (Russia); Grigory P. Panasenko (France) and Ruxandra Stavre (Romania); Sergei V. Poborchi (Russia); Jurgen Rossmann (Germany); Gunther Schmidt (Germany); Gregory C. Verchota (USA).

Ari Laptev
Imperial College London (UK) and
Royal Institute of Technology (Sweden)
Ari Laptev is a world-recognized specialist in Spectral Theory of
Differential Operators. He is the President of the European Mathematical
Society for the period 2007- 2010.

Tamara Rozhkovskaya
Sobolev Institute of Mathematics SB RAS (Russia)
and an independent publisher
Editors and Authors are exclusively invited to contribute to volumes highlighting
recent advances in various fields of mathematics by the Series Editor and a founder
of the IMS Tamara Rozhkovskaya.

Cover image: Vladimir Maz'ya

Author(s): Catherine Bandle, Vitaly Moroz (auth.), Ari Laptev (eds.)
Series: International Mathematical Series 12
Edition: 1
Publisher: Springer-Verlag New York
Year: 2010

Language: English
Pages: 386
Tags: Analysis; Partial Differential Equations; Functional Analysis

Front Matter....Pages i-xxii
Large Solutions to Semilinear Elliptic Equations with Hardy Potential and Exponential Nonlinearity....Pages 1-22
Stability Estimates for Resolvents, Eigenvalues, and Eigenfunctions of Elliptic Operators on Variable Domains....Pages 23-60
Operator Pencil in a Domain with Concentrated Masses. A Scalar Analog of Linear Hydrodynamics....Pages 61-94
Selfsimilar Perturbation near a Corner: Matching Versus Multiscale Expansions for a Model Problem....Pages 95-134
Stationary Navier–Stokes Equation on Lipschitz Domains in Riemannian Manifolds with Nonvanishing Boundary Conditions....Pages 135-144
On the Regularity of Nonlinear Subelliptic Equations....Pages 145-157
Rigorous and Heuristic Treatment of Sensitive Singular Perturbations Arising in Elliptic Shells....Pages 159-202
On the Existence of Positive Solutions of Semilinear Elliptic Inequalities on Riemannian Manifolds....Pages 203-218
Recurrence Relations for Orthogonal Polynomials and Algebraicity of Solutions of the Dirichlet Problem....Pages 219-228
On First Neumann Eigenvalue Bounds for Conformal Metrics....Pages 229-238
Necessary Condition for the Regularity of a Boundary Point for Porous Medium Equations with Coefficients of Kato Class....Pages 239-252
The Problem of Steady Flow over a Two-Dimensional Bottom Obstacle....Pages 253-274
Well Posedness and Asymptotic Expansion of Solution of Stokes Equation Set in a Thin Cylindrical Elastic Tube....Pages 275-301
On Solvability of Integral Equations for Harmonic Single Layer Potential on the Boundary of a Domain with Cusp....Pages 303-314
Hölder Estimates for Green’s Matrix of the Stokes System in Convex Polyhedra....Pages 315-336
Boundary Integral Methods for Periodic Scattering Problems....Pages 337-363
Boundary Coerciveness and the Neumann Problem for 4th Order Linear Partial Differential Operators....Pages 365-378
Back Matter....Pages 379-385