Potential Theory on Lipschitz Domains in Riemannian Manifolds: Sobolev–Besov Space Results and the Poisson Problem
✍ Scribed by Marius Mitrea; Michael Taylor
- Publisher
- Elsevier Science
- Year
- 2000
- Tongue
- English
- Weight
- 450 KB
- Volume
- 176
- Category
- Article
- ISSN
- 0022-1236
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✦ Synopsis
We continue a program to develop layer potential techniques for PDE on Lipschitz domains in Riemannian manifolds. Building on L p and Hardy space estimates established in previous papers, here we establish Sobolev and Besov space estimates on solutions to the Dirichlet and Neumann problems for the Laplace operator plus a potential, on a Lipschitz domain in a Riemannian manifold with a metric tensor smooth of class C 1+# , for some #>0. We treat the inhomogeneous problem and extend it to the setting of manifolds results obtained for the constantcoefficient Laplace operator on a Lipschitz domain in Euclidean space, with the Dirichlet boundary condition, by D. Jerison and C. Kenig.