| eBook ISBN: | 978-1-4704-3446-5 |
| Product Code: | MEMO/243/1149.E |
| List Price: | $83.00 |
| MAA Member Price: | $74.70 |
| AMS Member Price: | $49.80 |
| eBook ISBN: | 978-1-4704-3446-5 |
| Product Code: | MEMO/243/1149.E |
| List Price: | $83.00 |
| MAA Member Price: | $74.70 |
| AMS Member Price: | $49.80 |
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Book DetailsMemoirs of the American Mathematical SocietyVolume: 243; 2016; 110 ppMSC: Primary 35; Secondary 31; 46
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 \(L^p\) classes. The authors 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 \(L^p\) space automatically assures their solvability in an extended range of Besov spaces;
(3) Well-posedness for the non-homogeneous boundary value problems.
In particular, the authors 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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Table of Contents
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Chapters
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1. Introduction
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2. Definitions
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3. The Main Theorems
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4. Interpolation, Function Spaces and Elliptic Equations
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5. Boundedness of Integral Operators
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6. Trace Theorems
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7. Results for Lebesgue and Sobolev Spaces: Historic Account and some Extensions
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8. The Green’s Formula Representation for a Solution
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9. Invertibility of Layer Potentials and Well-Posedness of Boundary-Value Problems
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10. Besov Spaces and Weighted Sobolev Spaces
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Additional Material
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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 \(L^p\) classes. The authors 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 \(L^p\) space automatically assures their solvability in an extended range of Besov spaces;
(3) Well-posedness for the non-homogeneous boundary value problems.
In particular, the authors prove well-posedness of the non-homogeneous Dirichlet problem with data in Besov spaces for operators with real, not necessarily symmetric, coefficients.
-
Chapters
-
1. Introduction
-
2. Definitions
-
3. The Main Theorems
-
4. Interpolation, Function Spaces and Elliptic Equations
-
5. Boundedness of Integral Operators
-
6. Trace Theorems
-
7. Results for Lebesgue and Sobolev Spaces: Historic Account and some Extensions
-
8. The Green’s Formula Representation for a Solution
-
9. Invertibility of Layer Potentials and Well-Posedness of Boundary-Value Problems
-
10. Besov Spaces and Weighted Sobolev Spaces
