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The book systematically develops the nonlinear potential theory connected with the weighted Sobolev spaces, where the weight usually belongs to Muckenhoupt's class of Ap weights. These spaces occur as solutions spaces for degenerate elliptic partial differential equations. The Sobolev space theory covers results concerning approximation, extension, and interpolation, Sobolev and Poincaré inequalities, Maz'ya type embedding theorems, and isoperimetric inequalities. In the chapter devoted to potential theory, several weighted capacities are investigated. Moreover, "Kellogg lemmas" are established for various concepts of thinness. Applications of potential theory to weighted Sobolev spaces include quasi continuity of Sobolev functions, Poincaré inequalities, and spectral synthesis theorems.
Potential theory (Mathematics) --- Nonlinear theories --- Sobolev spaces --- Espaces de Sobolev --- Niet-lineaire theorieën --- Potentiaaltheorie --- Potentiel [Théorie du ] --- Ruimten van Sobolev --- Sobolev [Espaces de ] --- Sobolev [Ruimten van ] --- Spaces [Sobolev ] --- Theorieën [Niet-lineaire ] --- Théories non-linéaires --- Potential theory (Mathematics). --- Partial differential equations. --- Potential Theory. --- Partial Differential Equations. --- Partial differential equations --- Green's operators --- Green's theorem --- Potential functions (Mathematics) --- Potential, Theory of --- Mathematical analysis --- Mechanics
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Equilibrium and nonequilibrium properties of correlated many-body systems are of growing interest in many fields of physics, including condensed matter, dense plasmas, nuclear matter and particles. The most powerful and general method which applies equally to all these areas is given by quantum field theory.Written by the leading experts and understandable to non-specialists, this book provides an overview on the basic ideas and concepts of the method of nonequilibrium Green's functions. It is complemented by modern applications of the method to a variety of topics, such as optics and transpor
Many-body problem --- Green's functions --- Quantum theory --- Semiconductors --- Optics --- Coulomb fuctions --- Nuclear matter --- Matter, Nuclear --- Matter --- Nuclear structure --- Functions, Green's --- Functions, Induction --- Functions, Source --- Green functions --- Induction functions --- Source functions --- Differential equations --- Potential theory (Mathematics) --- Constitution
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