The topics covered in this volume are close to the scientific interests of Professor Maz'ya and focus on the current state of research in analysis, PDEs and function theory. All the results are new and have never before been published.

Topics of this volume are close to scientific interests of Professor Maz'ya and use, directly or indirectly, the fundamental influential Maz'ya's works penetrating, in a sense, the theory of PDEs.

In particular, recent advantages in the study of semilinear elliptic equations, stationary Navier-Stokes equations, the Stokes system in convex polyhedra, periodic scattering problems, problems with perturbed boundary at a conic point, singular perturbations arising in elliptic shells and other important problems in mathematical physics are presented.

Professor Maz'ya has received numerous awards for his outstanding contributions, in particular, the Humboldt Research Prize (1999), the Verdaguer Prize of the French Academy of Sciences (2003) He was elected to the Royal Society of Edinburgh (2001) and the Royal Swedish Academy of Sciences (2002) Several international conferences were organised for the occasion of his 60th birthday There are several collections of papers honored Prof. Maz'ya. Prof. Maz'ya published more than 20 monographs and more than 450 articles. The range of his interests is very wide and many of his results play a key role in many areas of analysis and PDEs. Nevertheless, the presented volume is absolutely different from all published books honored V. Maz'ya: It focuses on the current state of research in analysis, PDEs and function theory, detailing recent advances, selected in relation to Mazy'as results. All the results are new and never published earlier The mentioned collections present proceedings of conferences in honor of V. Maz'ya and contributors are participants of these conferences. In this volume contributors and contributions were selected in accordance with the main idea of the volume Includes supplementary material: sn.pub/extras

Klappentext

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

Inhalt
Large Solutions to Semilinear Elliptic Equations with Hardy Potential and Exponential Nonlinearity.- Stability Estimates for Resolvents, Eigenvalues, and Eigenfunctions of Elliptic Operators on Variable Domains.- Operator Pencil in a Domain with Concentrated Masses. A Scalar Analog of Linear Hydrodynamics.- Selfsimilar Perturbation near a Corner: Matching Versus Multiscale Expansions for a Model Problem.- Stationary Navier#x2013;Stokes Equation on Lipschitz Domains in Riemannian Manifolds with Nonvanishing Boundary Conditions.- On the Regularity of Nonlinear Subelliptic Equations.- Rigorous and Heuristic Treatment of Sensitive Singular Perturbations Arising in Elliptic Shells.- On the Existence of Positive Solutions of Semilinear Elliptic Inequalities on Riemannian Manifolds.- Recurrence Relations for Orthogonal Polynomials and Algebraicity of Solutions of the Dirichlet Problem.- On First Neumann Eigenvalue Bounds for Conformal Metrics.- Necessary Condition for the Regularity of a Boundary Point for Porous Medium Equations with Coefficients of Kato Class.- The Problem of Steady Flow over a Two-Dimensional Bottom Obstacle.- Well Posedness and Asymptotic Expansion of Solution of Stokes Equation Set in a Thin Cylindrical Elastic Tube.- On Solvability of Integral Equations for Harmonic Single Layer Potential on the Boundary of a Domain with Cusp.- H#x00F6;lder Estimates for Green#x2019;s Matrix of the Stokes System in Convex Polyhedra.- Boundary Integral Methods for Periodic Scattering Problems.- Boundary Coerciveness and the Neumann Problem for 4th Order Linear Partial Differential Operators.