Around the Research of Vladimir Maz'ya I - III: Function Spaces, Partial Differential Equations, Analysis and Applications

ISBN-13: 9781441913463 / Angielski / Twarda / 2010 / 1200 str.

Ari Laptev; Tamara Rozhkovskaya

Opis

Research articles and surveys from world-recognized mathematicians cover large areas in Analysis where the contributions of Prof. Maz'ya are fundamental, influential, and/or pioneering. Among more than 25 monographs and 450 research papers by V. Maz'ya, one can find deep results predetermining the further development of very diverse topics, which is reflected in the collected papers. Recent advantages in the theory of Sobolev spaces are presented. Hardy-Sobolev-Maz'ya inequalities, Maz'ya isocapacitary inequalities, isoperimetric inequalities, sharp constants, extension operators are generalized in various settings. Important PDEs are studied by methods of homogenization, multiscale expansion, matched asymptotic expansions, etc. Various problems in Analysis, like Beurling's minimum principle, inverse hyperbolic problems, degenerate oblique derivative problems and many other problems are treated. Archive photos representative, in particular, meetings of V. Maz'ya with S. Sobolev and with L. Schwarz are included. List of references to Maz'ya's works throughout the volumes companions the collection.

Spis treści

Around the Research of Vladimir Maz'ya I
Function Spaces

Hardy Inequalities for Nonconvex Domains, F. Avkhadiev, A. Laptev.- Distributions with Slow Tails and Ergodicity of Markov Semigroups in Infinite Dimensions, S. Bobkov, B. Zegarlinski.- On Some Aspects of the Theory of Orlicz-Sobolev Spaces, A. Cianchi.- Mellin Analysis of Weighted Sobolev Spaces with Nonhomogeneous Norms on Cones, M. Costabel et al.- Optimal Hardy-Sobolev-Maz'ya Inequalities with Multiple Interior Singularities, S. Filippas et al.- Sharp Fractional Hardy Inequalities in Half-Spaces, R.L. Frank, R. Seiringer.- Collapsing Riemannian Metrics to Sub-Riemannian and the Geometry of Hypersurfaces in Carnot Groups, N. Garofalo, C. Selby.- Sobolev Homeomorphisms and Composition Operators, V. Gol'dshtein, A. Ukhlov.- Extended L^p Dirichlet Spaces, N. Jacob, R.L. Schilling.- Characterizations for the Hardy Inequality, J. Kinnunen, R. Korte.- Geometric Properties of Planar BV-Extension Domains, P. Koskela et al.- On a New Characterization of Besov Spaces with Negative Exponents, M. Marcus, L. Véron.- Isoperimetric Hardy Type and Poincare Inequalities on Metric Spaces, J. Martin, M. Milman.- Gauge Functions and Sobolev Inequalities on Fluctuating Domains, E. Mbakop, U. Mosco.- A Converse to Maz'ya's Inequality for Capacities under Curvature Lower Bound, E. Milman.- Pseudo-Poincaré Inequalities and Applications to Sobolev Inequalities, L. Saloff-Coste.- The p-Faber-Krahn Inequality Noted, J. Xiao.

 

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

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.- Boundary Coerciveness and the Neumann Problem for 4th Order Linear Partial Differential Operators, G.C. Verchota.

 

Around the Research of Vladimir Maz'ya III
Analysis and Applications

Optimal Control of a Biharmonic Obstacle Problem, D. Adams et al.- Minimal Thinness and Beurling's Minimum Principle, H. Aikawa.- Progress in the Problem of L^p-Contractivity of Semigroups for Partial Differential Operators, A. Cialdea.- Uniqueness and Nonuniqueness in Inverse Hyperbolic Problems and the Black Hole Phenomenon, G. Eskin.- Global Green's Function Estimates, M.W. Frazier, I.E. Verbitsky.- On Spectral Minimal Partitions: the Case of the Sphere, B. Helffer et al.- Weighted Sobolev Space Estimates for a Class of Singular Integral Operators, D. Mitrea et al.- On general Cwikel-Lieb-Rozenblum and Lieb-Thirring inequalities, S. Molchanov, B. Vainberg.- Estimates for the Counting Function of the Laplace Operator on Domains with Rough Boundaries, Y. Netrusov, Y. Safarov.- W^2,p-Theory of the Poincaré Problem, D.K. Palagachev.- Weighted Inequalities for Integral and Supremum Operators, L. Pick.- Finite Rank Toeplitz Operators in the Bergman Space, G. Rozenblum.- Resolvent Estimates for Non-Selfadjoint Operators via Semigroups, J. Sjöstrand.