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

ISBN-13: 9781461425489 / Angielski / Miękka / 2012 / 386 str.

Ari Laptev

Opis

New results, presented from world-recognized experts, 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, the following topics are covered: semilinear elliptic equations with exponential monlinearity, stationary Navier-Stokes equations on Lipschitz domains in Riemannian manifolds, Stokes equations in a thin cylindrical elastic tube the Neumann problem for 4th order linear partial differential operators the Stokes system in convex polyhedra, periodic scattering problems, integral equations for harmonic single layer potential on the boundary of a domain with cusp. Homogenization methods, methods of multiscale expansions, matched asymptotic expansions are applied for studying PDEs, problems with perturbed boundary at a conic point, etc. Singular perturbations arising in elliptic shells, positive solutions of semilinear elliptic inequalities on Riemannian manifolds, the regularity for nonlinear subelliptic equations, and the regularity of boundary points are discussed.

Spis treści

Large Solutions to Semilinear Elliptic Equations with Hardy Potential and Exponential Nonlinearity, C. Bandle et al.- Stability Estimates for Resolvents, Eigenvalues, and Eigenfunctions of Elliptic Operators on Variable Domains, G. Barbatis et al.- Operator Pencil in a Domain with Concentrated Masses. A Scalar Analog of Linear Hydrodynamics, G. Chechkin.- Selfsimilar Perturbation near a Corner: Matching Versus Multiscale Expansions for a Model Problem, M. Dauge et al.- Stationary Navier-Stokes Equation on Lipschitz Domains in Riemannian Manifolds with Nonvanishing Boundary Conditions, M. Dindoš.- On the Regularity of Nonlinear Subelliptic Equations, A. Domokos, J.J. Manfredi.- Rigorous and Heuristic Treatment of Sensitive Singular Perturbations Arising in Elliptic Shells, Y.V. Egorov et al.- On the Existence of Positive Solutions of Semilinear Elliptic Inequalities on Riemannian Manifolds, A. Grigor'yan, V.A. Kondratiev.- Recurrence Relations for Orthogonal Polynomials and Algebraicity of Solutions of the Dirichlet Problem, D. Khavinson, N. Stylianopoulos.- On First Neumann Eigenvalue Bounds for Conformal Metrics, G. Kokarev, N. Nadirashvili.- Necessary Condition for the Regularity of a Boundary Point for Porous Medium Equations with Coefficients of Kato Class, V. Liskevich, I.I. Skrypnik.- The Problem of Steady Flow over a Two-Dimensional Bottom Obstacle, O. Motygin, N. Kuznetsov.- Well Posedness and Asymptotic Expansion of Solution of Stokes Equation Set in a Thin Cylindrical Elastic Tube, G.P. Panasenko, R. Stavre.- On Solvability of Integral Equations for Harmonic Single Layer Potential on the Boundary of a Domain with Cusp, S.V. Poborchi.- Holder Estimates for Green's Matrix of the Stokes System in Convex Polyhedra, J. Rossmann.- Boundary Integral Methods for Periodic Scattering Problems, G. Schmidt.- BoundaryCoerciveness and the Neumann Problem for 4th Order Linear Partial Differential Operators, G.C. Verchota.

Blurb

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