Document Type
Article
Date
12-27-2000
Disciplines
Mathematics
Description/Abstract
We show existence and uniqueness for the solutions of the regularity and the Neumann problems for harmonic functions on Lipschitz domains with data in the Hardy spaces Hp1,(partial D)(Hp (partial D)), p>2/3-E, where D C R2 and E is a (small) number depending on the Lipschitz nature of D. This in turn implies that solutions to the Dirichlet problem with data in the Holder class C1/2+E(partial D) are themselves in C1/2+E(D). Both of these results are sharp. In fact, we prove a more general statement regarding the Hp solvability for divergence form elliptic equations with bounded measurable coefficients.
We also prove H2/3-E and C1/2+E solvability result for the regularity and Dirichlet problem for the biharmonic equation on Lipschitz domains.
Recommended Citation
Stefanov, Atanas and Verchota, Gregory C., "Optimal Solvability for the Dirichlet and Neumann Problem in Dimension Two" (2000). Mathematics - All Scholarship. 135.
https://surface.syr.edu/mat/135
Source
Harvested from arXiv.org
Creative Commons License
This work is licensed under a Creative Commons Attribution 3.0 License.
Additional Information
This manuscript is from arXiv.org, for more information see http://arxiv.org/abs/math/0012254