The Dirichlet Problem with L2-Boundary Data for Elliptic Linear Equations [1 ed.] 3540544860, 9783540544869, 0387544860
The Dirichlet problem has a very long history in mathematics and its importance in partial differential equations, harmo
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English Pages 173 [177] Year 1991
Table of contents :
Introduction....Pages 1-4
Weighted Sobolev space $$\tilde W^{1,2}$$ ....Pages 7-19
The Dirichlet problem in a half-space....Pages 20-45
The Dirichlet problem in a bounded domain....Pages 46-66
Estimates of derivatives....Pages 67-77
Harmonic measure....Pages 78-89
Exceptional sets on the boundary....Pages 90-103
Applications of the L 2 -method....Pages 104-116
Domains with C 1,α -boundary....Pages 117-130
The space C n−1 ( $$\bar Q$$ )....Pages 131-141
C n−1 -estimate of the solution of the Dirichlet problem with L 2 -boundary data....Pages 142-167
Introduction....Pages 1-4
Weighted Sobolev space $$\tilde W^{1,2}$$ ....Pages 7-19
The Dirichlet problem in a half-space....Pages 20-45
The Dirichlet problem in a bounded domain....Pages 46-66
Estimates of derivatives....Pages 67-77
Harmonic measure....Pages 78-89
Exceptional sets on the boundary....Pages 90-103
Applications of the L 2 -method....Pages 104-116
Domains with C 1,α -boundary....Pages 117-130
The space C n−1 ( $$\bar Q$$ )....Pages 131-141
C n−1 -estimate of the solution of the Dirichlet problem with L 2 -boundary data....Pages 142-167
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