Sobolev Spaces in Mathematics III [electronic resource] : Applications in Mathematical Physics / edited by Victor Isakov.

Contributor(s): Isakov, Victor [editor.] | SpringerLink (Online service)
Material type: TextTextSeries: International Mathematical Series: 10Publisher: New York, NY : Springer New York, 2009Description: XXXII, 336 p. online resourceContent type: text Media type: computer Carrier type: online resourceISBN: 9780387856520Subject(s): Mathematics | Mathematical analysis | Analysis (Mathematics) | Functional analysis | Partial differential equations | Functions of real variables | Numerical analysis | Mathematical optimization | Mathematics | Analysis | Real Functions | Partial Differential Equations | Functional Analysis | Optimization | Numerical AnalysisAdditional physical formats: Printed edition:: No titleDDC classification: 515 LOC classification: QA299.6-433Online resources: Click here to access online
Contents:
Geometrization of Rings as a Method for Solving Inverse Problems -- The Ginzburg-Landau Equations for Superconductivity with Random Fluctuations -- Carleman Estimates with Second Large Parameter for Second Order Operators -- Sharp Spectral Asymptotics for Dirac Energy -- Linear Hyperbolic and Petrowski Type PDEs with Continuous Boundary Control ? Boundary Observation Open Loop Map: Implication on Nonlinear Boundary Stabilization with Optimal Decay Rates -- Uniform Asymptotics of Green's Kernels for Mixed and Neumann Problems in Domains with Small Holes and Inclusions -- Finsler Structures and Wave Propagation.
In: Springer eBooksSummary: 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).
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Geometrization of Rings as a Method for Solving Inverse Problems -- The Ginzburg-Landau Equations for Superconductivity with Random Fluctuations -- Carleman Estimates with Second Large Parameter for Second Order Operators -- Sharp Spectral Asymptotics for Dirac Energy -- Linear Hyperbolic and Petrowski Type PDEs with Continuous Boundary Control ? Boundary Observation Open Loop Map: Implication on Nonlinear Boundary Stabilization with Optimal Decay Rates -- Uniform Asymptotics of Green's Kernels for Mixed and Neumann Problems in Domains with Small Holes and Inclusions -- Finsler Structures and Wave Propagation.

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).

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