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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...
| Cote: | Libro Electrónico |
|---|---|
| Auteurs principaux: | , |
| Format: | Électronique eBook |
| Langue: | Inglés |
| Publié: |
Providence, Rhode Island :
American Mathematical Society,
2016.
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| Collection: | Memoirs of the American Mathematical Society ;
no. 1149. |
| Sujets: | |
| Accès en ligne: | Texto completo |
Table des matières:
- 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.