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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...

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Detalles Bibliográficos
Clasificación:Libro Electrónico
Autores principales: Barton, Ariel, 1982- (Autor), Mayboroda, Svitlana, 1981- (Autor)
Formato: Electrónico eBook
Idioma:Inglés
Publicado: Providence, Rhode Island : American Mathematical Society, 2016.
Colección:Memoirs of the American Mathematical Society ; no. 1149.
Temas:
Acceso en línea:Texto completo
Tabla de Contenidos:
  • 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.