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＜電子ブック＞
Integro-Differential Elliptic Equations / by Xavier Fernández-Real, Xavier Ros-Oton
(Progress in Mathematics. ISSN:2296505X ; 350)

版	1st ed. 2024.
出版者	(Cham : Springer Nature Switzerland : Imprint: Birkhäuser)
出版年	2024
本文言語	英語
大きさ	XVI, 395 p. 22 illus., 2 illus. in color : online resource
著者標目	*Fernández-Real, Xavier author Ros-Oton, Xavier author SpringerLink (Online service)
件　名	LCSH:Integral equations LCSH:Differential equations LCSH:Operator theory FREE:Integral Equations FREE:Differential Equations FREE:Operator Theory
一般注記	The square root of the Laplacian -- Linear integro-differential equations -- Fully nonlinear equations -- Obstacle problems This monograph offers a self-contained introduction to the regularity theory for integro-differential elliptic equations, mostly developed in the 21st century. This class of equations finds relevance in fields such as analysis, probability theory, mathematical physics, and in several contexts in the applied sciences. The work gives a detailed presentation of all the necessary techniques, with a primary focus on the main ideas rather than on proving all the results in their greatest generality. The basic building blocks are presented first, with the study of the square root of the Laplacian, and weak solutions to linear equations. Subsequently, the theory of viscosity solutions to nonlinear equations is developed, and proofs are provided for the main known results in this context. The analysis finishes with the investigation of obstacle problems for integro-differential operators and establishes the regularity of solutions and free boundaries. A distinctive feature of this work lies in its presentation of nearly all covered material in a monographic format for the first time, and several proofs streamline, and often simplify, those in the original papers. Furthermore, various open problems are listed throughout the chapters HTTP:URL=https://doi.org/10.1007/978-3-031-54242-8

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