Around the Research of Vladimir Maz'ya II: Partial Differential Equations (International Mathematical Series Book 12)

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 International Mathematical Series Volume 13Around the Research of Vladimir Ma'z'ya IIIAnalysis and ApplicationsEdited by Ari Laptev More than 450 research articles and 20 books by Prof. Maz'ya contain numerous fundamental results and fruitful techniques which have strongly influenced the development of many branches in Analysis and, in particular, the topics discussed in this volume: problems with biharmonic differential operators, the minimal thinness of nontangentially accessible domains, the Lp-dissipativity of partial differential operators and the Lp-contractivity of the generated semigroups, uniqueness and nonuniqueness in inverse hyperbolic problems and the existence of black (white) holes, global exponential bounds for Green's functions for differential and integral equations with possibly singular coefficients, data, and boundaries of the domains, properties of spectral minimal partitions, the boundedness of integral operators from Besov spaces on the boundary of a Lipschitz domain into weighted Sobolev spaces of functions in the domain, the Cwikel-Lieb-Rozenblum and Lieb-Thirring inequalities for operators on functions in metric spaces, spectral problems with the Schrodinger operator, the Weyl formula for the Laplace operator on a domain under minimal assumptions on the boundary, a degenerate oblique derivative problem for second order uniformly elliptic operators, weighted inequalities with the Hardy operator in the integral and supremum form, finite rank Toeplitz operators and applications, the resolvent of a non-selfadjoint pseudodifferential operator. Contributors include: David R. Adams (USA), Volodymyr Hrynkiv (USA), and Suzanne Lenhart (USA); Hiroaki Aikawa (Japan); Alberto Cialdea (Italy); Gregory Eskin (USA); Michael W. Frazier (USa) and Igor E. Verbitsky (USA); Bernard Helffer (France), Thomas Hoffmann-Ostenhof (Austria), and Susanna Terracini (italy); Dorina Mitrea (USA), Marius Mitrea (USA), and Sylvie Monniaux (France); Stanislav Molchanov (USA) and Boris Vainberg (USA); Yuri Netrusov (UK) and Yuri Safarov (UK); Dian K. Palagachev (Italy); Lubos Pick (Czech Republic); Grigori Rozenblum (Sweden); Johannes Sjostrand (France). Ari LaptevImperial College London (UK) andRoyal Institute of Technology (Sweden)Ari Laptev is a world-recognized specialist in Spectral Theory of Differential Operators. He is the President of the European MathematicalSociety for the period 2007- 2010. Tamara RozhkovskayaSobolev Institute of Mathematics SB RAS (Russia) and an independent publisherEditors and Authors are exclusively invited to contribute to volumes highlightingrecent advances in various fields of mathematics by the Series Editor and a founder of the IMS Tamara Rozhkovskaya. Cover image: Vladimir Maz'ya 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 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.