Sobolev spaces in mathematics II: applications in analysis and partial differential equations

Sobolev spaces become the established and universal language of partial differential equations and mathematical analysis. Among a huge variety of problems where Sobolev spaces are used, the following important topics are the focus ofthis volume: boundary value problems in domains with singularities, higher order partial differential equations, local polynomial approximations, inequalities in Sobolev-Lorentz spaces, function spaces in cellular domains, the spectrum of a Schrodinger operator with negative potential and other spectral problems, criteria for the complete integration of systems of differential equationswith applications to differential geometry, some aspects of differential forms on Riemannian manifolds related to Sobolev inequalities, Brownian motion on a Cartan-Hadamard manifold, etc. Two short biographical articles on the works of Sobolev in the 1930s and the foundation of Akademgorodok in Siberia, supplied with unique archive photos of S. Sobolev are included Presentation of new results on the latest topics of the theory Sobolev spaces, partial differentialequations, analysis and mathematical physics The authors and editors are world-known specialists, working in different countries INDICE: From the contents On the Mathematical Works of S.L. Sobolev in the1930s, V. Babich.- Sobolev in Siberia, Y. Reshetnyak.- Boundary Harnack Principle and the Quasihyperbolic Boundary Condition, H. Aikawa.- Sobolev Spaces and their Relatives: local Polynomial Approximation Approach, Y. Brudnyi.- Spectral Stability of Higher Order Uniformly Elliptic Operators, V. Burenkov, P.D. Lamberti.- Conductor Inequalities and Criteria for Sobolev - Lorentz Two - Weight Inequalities, S. Costea, V. Maz'ya.- Besov Regularity for the Poisson Equation in Smooth and Polyhedral Cones, S. Dahlke, W. Sickel.- Variational Approach to Complicated Similarity Solutions of Higher Order Nonlinear Evolution Partial Differential Equations, V. Galaktionov et al.- Lq,p-Cohomology of Riemannian Manifolds with Negative Curvature, V. Gol'dshtein, M. Troyanov.- Volume Growth and Escape Rate of Brownian Motion on a Cartan–Hadamard Manifold, A. Grigor'yan, E. Hsu.

• ISBN: 978-0-387-85649-0
• Editorial: Springer
• Encuadernacion: Cartoné
• Páginas: 415
• Fecha Publicación: 01/11/2008
• Nº Volúmenes: 1
• Idioma: Inglés