| Description |
1 online resource (v, 110 pages) : illustrations |
| Series |
Memoirs of the American Mathematical Society, 0065-9266 ; volume 243, number 1149 |
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Memoirs of the American Mathematical Society ; no. 1149.
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| Contents |
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 |
| Summary |
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 |
| Notes |
"Volume 243, number 1149 (second of 4 numbers), September 2016." |
| Bibliography |
Includes bibliographical references (pages 105-110) |
| Notes |
Online resource; title from PDF title page (viewed June 23, 2016) |
| Subject |
Boundary value problems.
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Elliptic operators.
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Besov spaces.
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Besov spaces
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Boundary value problems
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Elliptic operators
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| Form |
Electronic book
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| Author |
Mayboroda, Svitlana, 1981- author.
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American Mathematical Society, publisher.
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| LC no. |
2016037190 |
| ISBN |
9781470434465 |
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1470434466 |
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