Fernández-Real, Xavier. creator author. aut http://id.loc.gov/vocabulary/relators/aut Ros-Oton, Xavier. author. aut http://id.loc.gov/vocabulary/relators/aut SpringerLink (Online service) text sz 2024 1st ed. 2024. monographic eng

electronic

electronic resource

access XVI, 395 p. 22 illus., 2 illus. in color. online resource. 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. The square root of the Laplacian -- Linear integro-differential equations -- Fully nonlinear equations -- Obstacle problems. by Xavier Fernández-Real, Xavier Ros-Oton. Integral equations Differential equations Operator theory Integral Equations Differential Equations Operator Theory QA431 9783031542428 https://doi.org/10.1007/978-3-031-54242-8 https://doi.org/10.1007/978-3-031-54242-8 240424 20251030112008.0 978-3-031-54242-8