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This book, which is based on several courses of lectures given by the author at the Independent University of Moscow, is devoted to Sobolev-type spaces and boundary value problems for linear elliptic partial differential equations. Its main focus is on problems in non-smooth (Lipschitz) domains for strongly elliptic systems.   The author, who is a prominent expert in the theory of linear partial differential equations, spectral theory, and pseudodifferential operators, has included his own very recent findings in the present book.   The book is well suited as a modern graduate textbook, utilizing a thorough and clear format that strikes a good balance between the choice of material and the style of exposition. It can be used both as an introduction to recent advances in elliptic equations and boundary value problems, and as a valuable survey and reference work. It also includes a good deal of new and extremely useful material not available in standard textbooks to date.   Graduate and post-graduate students, as well as specialists working in the fields of partial differential equations, functional analysis, operator theory, and mathematical physics will find this book particularly valuable.

Mathematics. --- Partial Differential Equations. --- Functional Analysis. --- Operator Theory. --- Potential Theory. --- Integral Equations. --- Mathematical Physics. --- Functional analysis. --- Integral equations. --- Operator theory. --- Differential equations, partial. --- Potential theory (Mathematics). --- Mathématiques --- Analyse fonctionnelle --- Equations intégrales --- Théorie des opérateurs --- Potentiel, Théorie du --- Mathematics --- Physical Sciences & Mathematics --- Calculus --- Partial differential equations. --- Mathematical physics. --- Green's operators --- Green's theorem --- Potential functions (Mathematics) --- Potential, Theory of --- Mathematical analysis --- Mechanics --- Functional analysis --- Equations, Integral --- Functional equations --- Functional calculus --- Calculus of variations --- Integral equations --- Partial differential equations --- Sobolev spaces. --- Differential equations, Elliptic. --- Elliptic differential equations --- Elliptic partial differential equations --- Linear elliptic differential equations --- Differential equations, Linear --- Differential equations, Partial --- Spaces, Sobolev --- Function spaces --- Physical mathematics --- Physics

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This book describes mathematical techniques for integral transforms in a detailed but concise manner. The techniques are subsequently applied to the standard partial differential equations, such as the Laplace equation, the wave equation and elasticity equations. Green’s functions for beams, plates and acoustic media are also shown, along with their mathematical derivations. The Cagniard-de Hoop method for double inversion is described in detail, and 2D and 3D elastodynamic problems are treated in full. This new edition explains in detail how to introduce the branch cut for the multi-valued square root function. Further, an exact closed form Green’s function for torsional waves is presented, as well as an application technique of the complex integral, which includes the square root function and an application technique of the complex integral.

Engineering. --- Appl.Mathematics/Computational Methods of Engineering. --- Theoretical and Applied Mechanics. --- Integral Transforms, Operational Calculus. --- Integral Transforms. --- Engineering mathematics. --- Mechanics, applied. --- Ingénierie --- Mathématiques de l'ingénieur --- Civil & Environmental Engineering --- Engineering & Applied Sciences --- Applied Mathematics --- Civil Engineering --- Integral transforms. --- Green's functions. --- Functions, Green's --- Functions, Induction --- Functions, Source --- Green functions --- Induction functions --- Source functions --- Transform calculus --- Operational calculus. --- Applied mathematics. --- Mechanics. --- Mechanics, Applied. --- Integral equations --- Transformations (Mathematics) --- Differential equations --- Potential theory (Mathematics) --- Mathematical and Computational Engineering. --- Applied mechanics --- Engineering, Mechanical --- Engineering mathematics --- Engineering --- Engineering analysis --- Mathematical analysis --- Mathematics --- Operational calculus --- Electric circuits --- Classical mechanics --- Newtonian mechanics --- Physics --- Dynamics --- Quantum theory --- Mathematical analysis. --- Mathematical and Computational Engineering Applications. --- Engineering Mechanics. --- Integral Transforms and Operational Calculus. --- Data processing. --- 517.1 Mathematical analysis