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The topic of the inverse problems is of substantial and rapidly growing interest for many scientists and engineers. The second edition covers most important recent developments in the field of inverse problems, describing theoretical and computational methods, and emphasizing new ideas and techniques. It also reflects new changes since the first edition, including some corrections. This edition is considerably expanded, with some concepts such as pseudo-convexity, and proofs simplified. New material is added to reflect recent progress in theory of inverse problems. This book is intended for mathematicians working with partial differential equations and their applications, and physicists, geophysicists and engineers involved with experiments in nondestructive evaluation, seismic exploration, remote sensing and tomography.

Inverse problems (Differential equations) --- Differential equations, Partial. --- Partial differential equations --- Differential equations --- Global analysis (Mathematics). --- Computer science --- Analysis. --- Computational Mathematics and Numerical Analysis. --- Theoretical, Mathematical and Computational Physics. --- Mathematics. --- Computer mathematics --- Discrete mathematics --- Electronic data processing --- Analysis, Global (Mathematics) --- Differential topology --- Functions of complex variables --- Geometry, Algebraic --- Mathematics --- Mathematical analysis. --- Analysis (Mathematics). --- Computer mathematics. --- Mathematical physics. --- 517.1 Mathematical analysis --- Mathematical analysis --- Physical mathematics --- Physics

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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).

Interpolation spaces. --- Sobolev spaces. --- Sobolev, S. L. --(Sergei? L'vovich), --1908-1989. --- Mathematics --- Engineering & Applied Sciences --- Physical Sciences & Mathematics --- Calculus --- Applied Mathematics --- Function spaces. --- Spaces, Function --- Spaces, Sobolev --- Mathematics. --- Mathematical analysis. --- Analysis (Mathematics). --- Functional analysis. --- Partial differential equations. --- Functions of real variables. --- Numerical analysis. --- Mathematical optimization. --- Analysis. --- Real Functions. --- Partial Differential Equations. --- Functional Analysis. --- Optimization. --- Numerical Analysis. --- Optimization (Mathematics) --- Optimization techniques --- Optimization theory --- Systems optimization --- Mathematical analysis --- Maxima and minima --- Operations research --- Simulation methods --- System analysis --- Real variables --- Functions of complex variables --- Partial differential equations --- Functional calculus --- Calculus of variations --- Functional equations --- Integral equations --- 517.1 Mathematical analysis --- Math --- Science --- Functional analysis --- Function spaces --- Global analysis (Mathematics). --- Differential equations, partial. --- Analysis, Global (Mathematics) --- Differential topology --- Geometry, Algebraic --- Sobolev spaces --- Interpolation spaces --- Sobolev, S L - (Sergeĭ Lʹvovich), - 1908-1989

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This third edition expands upon the earlier edition by adding nearly 40 pages of new material reflecting the analytical and numerical progress in inverse problems in last 10 years.  As in the second edition, the emphasis is on new ideas and methods rather than technical improvements. These new ideas include use of the stationary phase method in the two-dimensional elliptic problems and of multi frequenciesemporal data to improve stability and numerical resolution. There are also numerous corrections and improvements of the exposition throughout. This book is intended for mathematicians working with partial differential equations and their applications, physicists, geophysicists, and financial, electrical, and mechanical engineers involved with nondestructive evaluation, seismic exploration, remote sensing, and various kinds of tomography. Review of the second edition: "The first edition of this excellent book appeared in 1998 and became a standard reference for everyone interested in analysis and numerics of inverse problems in partial differential equations. … The second edition is considerably expanded and reflects important recent developments in the field … . Some of the research problems from the first edition have been solved … ." (Johannes Elschner, Zentralblatt MATH, Vol. 1092 (18), 2006).

Partial differential equations --- Differential equations --- Mathematics --- Geodesy. Cartography --- Mathematical physics --- Computer. Automation --- differentiaalvergelijkingen --- fotogrammetrie --- theoretische fysica --- remote sensing --- informatica --- externe fixatie (geneeskunde --- wiskunde --- Partial differential equations. --- Computer mathematics. --- Mathematical physics. --- Remote sensing. --- Partial Differential Equations. --- Computational Mathematics and Numerical Analysis. --- Theoretical, Mathematical and Computational Physics. --- Remote Sensing/Photogrammetry. --- Remote-sensing imagery --- Remote sensing systems --- Remote terrain sensing --- Sensing, Remote --- Terrain sensing, Remote --- Aerial photogrammetry --- Aerospace telemetry --- Detectors --- Space optics --- Physical mathematics --- Physics --- Computer mathematics --- Electronic data processing

Choose an application

• Reference Manager
• EndNote
• RefWorks (Direct export to RefWorks)

Choose an application

• Reference Manager
• EndNote
• RefWorks (Direct export to RefWorks)

This third edition expands upon the earlier edition by adding nearly 40 pages of new material reflecting the analytical and numerical progress in inverse problems in last 10 years.  As in the second edition, the emphasis is on new ideas and methods rather than technical improvements. These new ideas include use of the stationary phase method in the two-dimensional elliptic problems and of multi frequenciesemporal data to improve stability and numerical resolution. There are also numerous corrections and improvements of the exposition throughout. This book is intended for mathematicians working with partial differential equations and their applications, physicists, geophysicists, and financial, electrical, and mechanical engineers involved with nondestructive evaluation, seismic exploration, remote sensing, and various kinds of tomography. Review of the second edition: "The first edition of this excellent book appeared in 1998 and became a standard reference for everyone interested in analysis and numerics of inverse problems in partial differential equations. … The second edition is considerably expanded and reflects important recent developments in the field … . Some of the research problems from the first edition have been solved … ." (Johannes Elschner, Zentralblatt MATH, Vol. 1092 (18), 2006).

Partial differential equations --- Differential equations --- Mathematics --- Geodesy. Cartography --- Mathematical physics --- Computer. Automation --- differentiaalvergelijkingen --- fotogrammetrie --- theoretische fysica --- remote sensing --- informatica --- externe fixatie (geneeskunde --- wiskunde