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Mathematics - Analysis | Sobolev Spaces in Mathematics III

Sobolev Spaces in Mathematics III

Applications in Mathematical Physics

Isakov, Victor (Ed.)

Jointly published with Tamara Rozhkovskaya Publisher, Novosibirsk, Russia

2009, XXXII, 336 p.

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  • Presentation of new results on the latest topics of the theory of Sobolev spaces, partial differential equations, analysis and mathematical physics
  • The authors and editors are world-renowned specialists working in different countries
  • Publication on the centenary of Sobolev’s birth with two short biographical articles and unique archive photos of S. Sobolev which have not yet been published in the English-language literature

The mathematical works of S.L.Sobolev were strongly motivated by particular problems coming from applications. In his celebrated book Applications of Functional Analysis in Mathematical Physics, 1950 and other works, S.Sobolev introduced general methods that turned out to be very influential in the study of mathematical physics in the second half of the XXth century. This volume, dedicated to the centenary of S.L. Sobolev, presents the latest results on some important problems of mathematical physics describing, in particular, phenomena of superconductivity with random fluctuations, wave propagation, perforated domains and bodies with defects of different types, spectral asymptotics for Dirac energy, Lam\'e system with residual stress, optimal control problems for partial differential equations and inverse problems admitting numerous interpretations. Methods of modern functional analysis are essentially used in the investigation of these problems.

Contributors include: Mikhail Belishev (Russia); Andrei Fursikov (Russia), Max Gunzburger (USA), and Janet Peterson (USA); Victor Isakov (USA) and Nanhee Kim (USA); Victor Ivrii (Canada); Irena Lasiecka (USA) and Roberto Triggiani (USA); Vladimir Maz'ya (USA-UK-Sweden) and Alexander Movchan (UK); Michael Taylor (USA)

Content Level » Research

Keywords » Ginzburg-Landau model - Sobolev space - asymptotic approximation - calculus - functional analysis - inverse problems - optimal control - partial differential equation - wave propagation

Related subjects » Analysis - Computational Science & Engineering - Dynamical Systems & Differential Equations - Mathematics

Table of contents / Preface / Sample pages 

Geometrization of Rings as a Method for Solving Inverse Problems, M. Belishev.- The Ginzburg–Landau Equations for Superconductivity with Random Fluctuations, A. Fursikov et al.- Carleman Estimates with Second Large Parameter for Second Order Operators, V. Isakov, N. Kim.- Sharp Spectral Asymptotics for Dirac Energy, V. Ivrii.- Linear Hyperbolic and Petrowski Type PDEs with Continuous Boundary Control - Boundary Observation Open Loop Map: Implication on Nonlinear Boundary Stabilization with Optimal Decay Rates, I. Lasiecka, R. Triggiani.- Uniform Asymptotics of Green's Kernels for Mixed and Neumann Problems in Domains with Small Holes and Inclusions, V. Maz'ya, A. Movchan.- Finsler Structures and Wave Propagation, M. Taylor.

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