Ebook: Sobolev Spaces in Mathematics II: Applications in Analysis and Partial Differential Equations
- Tags: Analysis, Partial Differential Equations, Functional Analysis, Optimization, Numerical Analysis
- Series: International Mathematical Series 9
- Year: 2009
- Publisher: Springer-Verlag New York
- Edition: 1
- Language: English
- pdf
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 in the focus of this 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 integrability of systems of differential equations with 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 1930's and foundation of Akademgorodok in Siberia, supplied with unique archive photos of S. Sobolev are included.
Contributors include: Vasilii Babich (Russia); Yuri Reshetnyak (Russia); Hiroaki Aikawa (Japan); Yuri Brudnyi (Israel); Victor Burenkov (Italy) and Pier Domenico Lamberti (Italy); Serban Costea (Canada) and Vladimir Maz'ya (USA-UK-Sweden); Stephan Dahlke (Germany) and Winfried Sickel (Germany); Victor Galaktionov (UK), Enzo Mitidieri (Italy), and Stanislav Pokhozhaev (Russia); Vladimir Gol'dshtein (Israel) and Marc Troyanov (Switzerland); Alexander Grigor'yan (Germany) and Elton Hsu (USA); Tunde Jakab (USA), Irina Mitrea (USA), and Marius Mitrea (USA); Sergey Nazarov (Russia); Grigori Rozenblum (Sweden) and Michael Solomyak (Israel); Hans Triebel (Germany)
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 in the focus of this 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 integrability of systems of differential equations with 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 1930's and foundation of Akademgorodok in Siberia, supplied with unique archive photos of S. Sobolev are included.
Contributors include: Vasilii Babich (Russia); Yuri Reshetnyak (Russia); Hiroaki Aikawa (Japan); Yuri Brudnyi (Israel); Victor Burenkov (Italy) and Pier Domenico Lamberti (Italy); Serban Costea (Canada) and Vladimir Maz'ya (USA-UK-Sweden); Stephan Dahlke (Germany) and Winfried Sickel (Germany); Victor Galaktionov (UK), Enzo Mitidieri (Italy), and Stanislav Pokhozhaev (Russia); Vladimir Gol'dshtein (Israel) and Marc Troyanov (Switzerland); Alexander Grigor'yan (Germany) and Elton Hsu (USA); Tunde Jakab (USA), Irina Mitrea (USA), and Marius Mitrea (USA); Sergey Nazarov (Russia); Grigori Rozenblum (Sweden) and Michael Solomyak (Israel); Hans Triebel (Germany)
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 in the focus of this 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 integrability of systems of differential equations with 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 1930's and foundation of Akademgorodok in Siberia, supplied with unique archive photos of S. Sobolev are included.
Contributors include: Vasilii Babich (Russia); Yuri Reshetnyak (Russia); Hiroaki Aikawa (Japan); Yuri Brudnyi (Israel); Victor Burenkov (Italy) and Pier Domenico Lamberti (Italy); Serban Costea (Canada) and Vladimir Maz'ya (USA-UK-Sweden); Stephan Dahlke (Germany) and Winfried Sickel (Germany); Victor Galaktionov (UK), Enzo Mitidieri (Italy), and Stanislav Pokhozhaev (Russia); Vladimir Gol'dshtein (Israel) and Marc Troyanov (Switzerland); Alexander Grigor'yan (Germany) and Elton Hsu (USA); Tunde Jakab (USA), Irina Mitrea (USA), and Marius Mitrea (USA); Sergey Nazarov (Russia); Grigori Rozenblum (Sweden) and Michael Solomyak (Israel); Hans Triebel (Germany)
Content:
Front Matter....Pages i-xxx
On the Mathematical Works of S.L. Sobolev in the 1930s....Pages 1-9
Sobolev in Siberia....Pages 11-17
Boundary Harnack Principle and the Quasihyperbolic Boundary Condition....Pages 19-30
Sobolev Spaces and their Relatives: Local Polynomial Approximation Approach....Pages 31-68
Spectral Stability of Higher Order Uniformly Elliptic Operators....Pages 69-102
Conductor Inequalities and Criteria for Sobolev-Lorentz Two-Weight Inequalities....Pages 103-121
Besov Regularity for the Poisson Equation in Smooth and Polyhedral Cones....Pages 123-145
Variational Approach to Complicated Similarity Solutions of Higher Order Nonlinear Evolution Partial Differential Equations....Pages 147-197
L q,p -Cohomology of Riemannian Manifolds with Negative Curvature....Pages 199-208
Volume Growth and Escape Rate of Brownian Motion on a Cartan—Hadamard Manifold....Pages 209-225
Sobolev Estimates for the Green Potential Associated with the Robin—Laplacian in Lipschitz Domains Satisfying a Uniform Exterior Ball Condition....Pages 227-260
Properties of Spectra of Boundary Value Problems in Cylindrical and Quasicylindrical Domains....Pages 261-309
Estimates for Completely Integrable Systems of Differential Operators and Applications....Pages 311-327
Counting Schr?dinger Boundstates: Semiclassics and Beyond....Pages 329-353
Function Spaces on Cellular Domains....Pages 355-385
Back Matter....Pages 387-388
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 in the focus of this 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 integrability of systems of differential equations with 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 1930's and foundation of Akademgorodok in Siberia, supplied with unique archive photos of S. Sobolev are included.
Contributors include: Vasilii Babich (Russia); Yuri Reshetnyak (Russia); Hiroaki Aikawa (Japan); Yuri Brudnyi (Israel); Victor Burenkov (Italy) and Pier Domenico Lamberti (Italy); Serban Costea (Canada) and Vladimir Maz'ya (USA-UK-Sweden); Stephan Dahlke (Germany) and Winfried Sickel (Germany); Victor Galaktionov (UK), Enzo Mitidieri (Italy), and Stanislav Pokhozhaev (Russia); Vladimir Gol'dshtein (Israel) and Marc Troyanov (Switzerland); Alexander Grigor'yan (Germany) and Elton Hsu (USA); Tunde Jakab (USA), Irina Mitrea (USA), and Marius Mitrea (USA); Sergey Nazarov (Russia); Grigori Rozenblum (Sweden) and Michael Solomyak (Israel); Hans Triebel (Germany)
Content:
Front Matter....Pages i-xxx
On the Mathematical Works of S.L. Sobolev in the 1930s....Pages 1-9
Sobolev in Siberia....Pages 11-17
Boundary Harnack Principle and the Quasihyperbolic Boundary Condition....Pages 19-30
Sobolev Spaces and their Relatives: Local Polynomial Approximation Approach....Pages 31-68
Spectral Stability of Higher Order Uniformly Elliptic Operators....Pages 69-102
Conductor Inequalities and Criteria for Sobolev-Lorentz Two-Weight Inequalities....Pages 103-121
Besov Regularity for the Poisson Equation in Smooth and Polyhedral Cones....Pages 123-145
Variational Approach to Complicated Similarity Solutions of Higher Order Nonlinear Evolution Partial Differential Equations....Pages 147-197
L q,p -Cohomology of Riemannian Manifolds with Negative Curvature....Pages 199-208
Volume Growth and Escape Rate of Brownian Motion on a Cartan—Hadamard Manifold....Pages 209-225
Sobolev Estimates for the Green Potential Associated with the Robin—Laplacian in Lipschitz Domains Satisfying a Uniform Exterior Ball Condition....Pages 227-260
Properties of Spectra of Boundary Value Problems in Cylindrical and Quasicylindrical Domains....Pages 261-309
Estimates for Completely Integrable Systems of Differential Operators and Applications....Pages 311-327
Counting Schr?dinger Boundstates: Semiclassics and Beyond....Pages 329-353
Function Spaces on Cellular Domains....Pages 355-385
Back Matter....Pages 387-388
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