03190nam a22005055i 4500001001800000003000900018005001700027007001500044008004100059020003700100024003500137050001000172072001700182072002300199072001600222100009400238245011500332250001800447264007300465300006400538336002600602337002600628338003600654347002400690490004700714505012900761520124800890650002402138650002802162650002102190650002402211650002802235650002102263700008602284710003402370773002602404776003602430776003602466776003602502830005402538856004602592912001402638912001502652999001702667978-3-031-54242-8DE-He21320251030112008.0cr nn 008mamaa240424s2024    sz |    s    |||| 0|eng d  a97830315424289978-3-031-54242-87 a10.1007/978-3-031-54242-82doi 4aQA431 7aPBKL2bicssc 7aMAT0340002bisacsh 7aPBKL2thema1 aFernández-Real, Xavier.eauthor.4aut4http://id.loc.gov/vocabulary/relators/aut97567510aIntegro-Differential Elliptic Equationsh[electronic resource] /cby Xavier Fernández-Real, Xavier Ros-Oton.  a1st ed. 2024. 1aCham :bSpringer Nature Switzerland :bImprint: Birkhäuser,c2024.  aXVI, 395 p. 22 illus., 2 illus. in color.bonline resource.  atextbtxt2rdacontent  acomputerbc2rdamedia  aonline resourcebcr2rdacarrier  atext filebPDF2rda1 aProgress in Mathematics,x2296-505X ;v3500 aThe square root of the Laplacian -- Linear integro-differential equations -- Fully nonlinear equations -- Obstacle problems.  aThis 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. 0aIntegral equations. 0aDifferential equations. 0aOperator theory.14aIntegral Equations.24aDifferential Equations.24aOperator Theory.1 aRos-Oton, Xavier.eauthor.4aut4http://id.loc.gov/vocabulary/relators/aut9756762 aSpringerLink (Online service)0 tSpringer Nature eBook08iPrinted edition:z978303154241108iPrinted edition:z978303154243508iPrinted edition:z9783031542442 0aProgress in Mathematics,x2296-505X ;v35097478640uhttps://doi.org/10.1007/978-3-031-54242-8  aZDB-2-SMA  aZDB-2-SXMS  c59342d59342