Elliptic Partial Differential Equations
Volume 1: Fredholm Theory of Elliptic Problems in Unbounded Domains

Authors: Vitaly Volpert



Offers a systematic investigation of general elliptic problems applicable both for bounded and unbounded domains

Includes a focus on unbounded domains, which has not been sufficiently presented in the existing literature

Gives a mostly self-contained presentation of the results

The theory of elliptic partial differential equations has undergone an important development over the last two centuries. Together with electrostatics, heat and mass diffusion, hydrodynamics and many other applications, it has become one of the most richly enhanced fields of mathematics. This monograph undertakes a systematic presentation of the theory of general elliptic operators. The author discusses a priori estimates, normal solvability, the Fredholm property, the index of an elliptic operator, operators with a parameter, and nonlinear Fredholm operators. Particular attention is paid to elliptic problems in unbounded domains which have not yet been sufficiently treated in the literature and which require some special approaches. The book also contains an analysis of non-Fredholm operators and discrete operators as well as extensive historical and bibliographical comments.

The selected topics and the author's level of discourse will make this book a most useful resource for researchers and graduate students working in the broad field of partial differential equations and applications.

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