Document Type

Article

Date

12-27-2000

Embargo Period

11-17-2011

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.

Additional Information

This manuscript is from arXiv.org, for more information see http://arxiv.org/abs/math/0012254

Source

Harvested from arXiv.org

Creative Commons License

Creative Commons Attribution 3.0 License
This work is licensed under a Creative Commons Attribution 3.0 License.

Included in

Mathematics Commons

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