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020 _a9783031542428
_9978-3-031-54242-8
024 7 _a10.1007/978-3-031-54242-8
_2doi
050 4 _aQA431
072 7 _aPBKL
_2bicssc
072 7 _aMAT034000
_2bisacsh
072 7 _aPBKL
_2thema
100 1 _aFernández-Real, Xavier.
_eauthor.
_4aut
_4http://id.loc.gov/vocabulary/relators/aut
_975675
245 1 0 _aIntegro-Differential Elliptic Equations
_h[electronic resource] /
_cby Xavier Fernández-Real, Xavier Ros-Oton.
250 _a1st ed. 2024.
264 1 _aCham :
_bSpringer Nature Switzerland :
_bImprint: Birkhäuser,
_c2024.
300 _aXVI, 395 p. 22 illus., 2 illus. in color.
_bonline resource.
336 _atext
_btxt
_2rdacontent
337 _acomputer
_bc
_2rdamedia
338 _aonline resource
_bcr
_2rdacarrier
347 _atext file
_bPDF
_2rda
490 1 _aProgress in Mathematics,
_x2296-505X ;
_v350
505 0 _aThe square root of the Laplacian -- Linear integro-differential equations -- Fully nonlinear equations -- Obstacle problems.
520 _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.
650 0 _aIntegral equations.
650 0 _aDifferential equations.
650 0 _aOperator theory.
650 1 4 _aIntegral Equations.
650 2 4 _aDifferential Equations.
650 2 4 _aOperator Theory.
700 1 _aRos-Oton, Xavier.
_eauthor.
_4aut
_4http://id.loc.gov/vocabulary/relators/aut
_975676
710 2 _aSpringerLink (Online service)
773 0 _tSpringer Nature eBook
776 0 8 _iPrinted edition:
_z9783031542411
776 0 8 _iPrinted edition:
_z9783031542435
776 0 8 _iPrinted edition:
_z9783031542442
830 0 _aProgress in Mathematics,
_x2296-505X ;
_v350
_974786
856 4 0 _uhttps://doi.org/10.1007/978-3-031-54242-8
912 _aZDB-2-SMA
912 _aZDB-2-SXMS
999 _c59342
_d59342