Optimal solvability for the Dirichlet and Neumann problem in dimension two
| dc.creator | Stefanov, Atanas | |
| dc.creator | Verchota, Gregory | |
| dc.date | 2000-12-27 | |
| dc.date.accessioned | 2026-07-07T04:39:25Z | |
| dc.date.available | 2026-07-07T04:39:25Z | |
| dc.description | 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 H^p, p>2/3, where This in turn implies that solutions to the Dirichlet problem with data in the Holder class C^{1/2}(\partial D) are themselves in C^{1/2}(D). Both of these results are sharp. In fact, we prove a more general statement regarding the H^p solvability for divergence form elliptic equations with bounded measurable coefficients. We also prove similar solvability result for the regularity and Dirichlet problem for the biharmonic equation on Lipschitz domains. | |
| dc.identifier | https://arxiv.org/abs/math/0012254 | |
| dc.identifier | http://arxiv.org/abs/math/0012254 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/60655 | |
| dc.subject | Classical Analysis and ODEs | |
| dc.subject | 35J25 | |
| dc.title | Optimal solvability for the Dirichlet and Neumann problem in dimension two | |
| dc.type | text |