Layer potentials and boundary-value problems for second order elliptic operators with data in Besov spaces /
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 potential...
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| Main Authors: | , |
|---|---|
| Format: | Electronic eBook |
| Language: | English |
| Published: |
Providence, Rhode Island :
American Mathematical Society,
2016.
|
| Series: | Memoirs of the American Mathematical Society ;
no. 1149. |
| Subjects: | |
| Online Access: |
Full text (Emmanuel users only) |
MARC
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| 100 | 1 | |a Barton, Ariel, |d 1982- |e author. | |
| 245 | 1 | 0 | |a Layer potentials and boundary-value problems for second order elliptic operators with data in Besov spaces / |c Ariel Barton, Svitlana Mayboroda. |
| 246 | 1 | |i Title from HTML article page: |a Layer potentials and boundary-value problems for second order ellipti operators with data in Besov spaces | |
| 264 | 1 | |a Providence, Rhode Island : |b American Mathematical Society, |c 2016. | |
| 264 | 4 | |c ©2016 | |
| 300 | |a 1 online resource (v, 110 pages) : |b illustrations | ||
| 336 | |a text |b txt |2 rdacontent | ||
| 337 | |a computer |b c |2 rdamedia | ||
| 338 | |a online resource |b cr |2 rdacarrier | ||
| 490 | 1 | |a Memoirs of the American Mathematical Society, |x 0065-9266 ; |v volume 243, number 1149 | |
| 500 | |a "Volume 243, number 1149 (second of 4 numbers), September 2016." | ||
| 504 | |a Includes bibliographical references (pages 105-110). | ||
| 505 | 0 | |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. | |
| 520 | |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. | ||
| 588 | 0 | |a Online resource; title from PDF title page (viewed June 23, 2016). | |
| 650 | 0 | |a Boundary value problems. | |
| 650 | 0 | |a Elliptic operators. | |
| 650 | 0 | |a Besov spaces. | |
| 700 | 1 | |a Mayboroda, Svitlana, |d 1981- |e author. | |
| 710 | 2 | |a American Mathematical Society, |e publisher. | |
| 758 | |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 |
| 830 | 0 | |a Memoirs of the American Mathematical Society ; |v no. 1149. | |
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