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|a 1262674070
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|a 515/.35
|2 23
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|a UAMI
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|a Barton, Ariel,
|d 1982-
|e author.
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|a Layer potentials and boundary-value problems for second order elliptic operators with data in Besov spaces /
|c Ariel Barton, Svitlana Mayboroda.
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|i Title from HTML article page:
|a Layer potentials and boundary-value problems for second order ellipti operators with data in Besov spaces
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|a Providence, Rhode Island :
|b American Mathematical Society,
|c 2016.
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|c ©2016
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300 |
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|a 1 online resource (v, 110 pages) :
|b illustrations
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|a text
|b txt
|2 rdacontent
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|a computer
|b c
|2 rdamedia
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|a online resource
|b cr
|2 rdacarrier
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|a Memoirs of the American Mathematical Society,
|x 0065-9266 ;
|v volume 243, number 1149
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588 |
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|a Online resource; title from PDF title page (viewed June 23, 2016).
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|a "Volume 243, number 1149 (second of 4 numbers), September 2016."
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|a Includes bibliographical references (pages 105-110).
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|a Introduction. History of the problem: Lp setting ; The nature of the problem and our main results ; Outline of the monograph ; Acknowledgements -- Definitions. Function spaces ; Elliptic equations ; Layer potentials ; Boundary-value problems -- The main theorems. Sharpness of these results -- Interpolation, function spaces and elliptic equations. Interpolation functors ; Function spaces ; Solutions to elliptic equations -- Boundedness of integral operators. Boundedness of the Newton potential ; Boundedness of the double and single layer potentials -- Trace theorems -- Results for Lebesgue and Sobolev spaces: historic account and some extensions -- The Green's Formula representation for a solution -- Invertibility of layer potentials and well-posedness of boundary-value problems. Invertibility and well-posedness: theorems 3.16, 3.17 and 3.18 ; Invertibility and functional analysis: corollaries 3.19, 3.20, and 3.21 ; Extrapolation of well-posedness and real coefficients: corollaries 3.23 and 3.24 -- Besov spaces and weighted Sobolev spaces -- Bibliography.
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|a This monograph presents a comprehensive treatment of second order divergence form elliptic operators with bounded measurable t-independent coefficients in spaces of fractional smoothness, in Besov and weighted Lp classes. We establish: (1) Mapping properties for the double and single layer potentials, as well as the Newton potential; (2) Extrapolation-type solvability results: the fact that solvability of the Dirichlet or Neumann boundary value problem at any given Lp space automatically assures their solvability in an extended range of Besov spaces; (3) Well-posedness for the non-homogeneous boundary value problems. In particular, we prove well-posedness of the non-homogeneous Dirichlet problem with data in Besov spaces for operators with real, not necessarily symmetric coefficients.
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590 |
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|a ProQuest Ebook Central
|b Ebook Central Academic Complete
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650 |
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|a Boundary value problems.
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650 |
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|a Elliptic operators.
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650 |
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|a Besov spaces.
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650 |
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|a Problèmes aux limites.
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650 |
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|a Opérateurs elliptiques.
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650 |
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|a Espaces de Besov.
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650 |
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|a Besov spaces
|2 fast
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650 |
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|a Boundary value problems
|2 fast
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650 |
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|a Elliptic operators
|2 fast
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1 |
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|a Mayboroda, Svitlana,
|d 1981-
|e author.
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710 |
2 |
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|a American Mathematical Society,
|e publisher.
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758 |
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|i has work:
|a Layer potentials and boundary-value problems for second order elliptic operators with data in Besov spaces (Text)
|1 https://id.oclc.org/worldcat/entity/E39PCGK9JB9CQkPfyBp7dq7pMX
|4 https://id.oclc.org/worldcat/ontology/hasWork
|
776 |
0 |
8 |
|i Print version:
|a Barton, Ariel, 1982-
|t Layer potentials and boundary-value problems for second order elliptic operators with data in Besov spaces.
|d Providence, Rhode Island : American Mathematical Society, 2016
|z 9781470419899
|w (DLC) 2016030522
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830 |
|
0 |
|a Memoirs of the American Mathematical Society ;
|v no. 1149.
|
856 |
4 |
0 |
|u https://ebookcentral.uam.elogim.com/lib/uam-ebooks/detail.action?docID=4901868
|z Texto completo
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938 |
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