03403nam a22005535i 4500 978-3-031-54242-8 DE-He213 20251030112008.0 cr nn 008mamaa 240424s2024 sz | s |||| 0|eng d 9783031542428 978-3-031-54242-8 10.1007/978-3-031-54242-8 doi QA431 PBKL bicssc MAT034000 bisacsh PBKL thema Fernández-Real, Xavier. author. aut http://id.loc.gov/vocabulary/relators/aut 75675 Integro-Differential Elliptic Equations [electronic resource] / by Xavier Fernández-Real, Xavier Ros-Oton. 1st ed. 2024. Cham : Springer Nature Switzerland : Imprint: Birkhäuser, 2024. XVI, 395 p. 22 illus., 2 illus. in color. online resource. text txt rdacontent computer c rdamedia online resource cr rdacarrier text file PDF rda Progress in Mathematics, 2296-505X ; 350 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. Integral equations. Differential equations. Operator theory. Integral Equations. Differential Equations. Operator Theory. Ros-Oton, Xavier. author. aut http://id.loc.gov/vocabulary/relators/aut 75676 SpringerLink (Online service) Springer Nature eBook Printed edition: 9783031542411 Printed edition: 9783031542435 Printed edition: 9783031542442 Progress in Mathematics, 2296-505X ; 350 74786 https://doi.org/10.1007/978-3-031-54242-8 ZDB-2-SMA ZDB-2-SXMS 59342 59342