Optimal solvability for the Dirichlet and Neumann problem in dimension two

Details Optimal solvability for the Dirichlet and Neumann problem in dimension two Optimal solvability for the Dirichlet and Neumann problem in dimension two

2000-12-27

arxiv.org/abs/math/0012254v1

Mathematics

Classical Analysis and ODEs

Scientific paper

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.

Affiliated with

Also associated with

No associations

Rating

Optimal solvability for the Dirichlet and Neumann problem in dimension two does not yet have a rating. At this time, there are no reviews or comments for this scientific paper.

If you have personal experience with Optimal solvability for the Dirichlet and Neumann problem in dimension two, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and Optimal solvability for the Dirichlet and Neumann problem in dimension two will most certainly appreciate the feedback.

Rate now

Comments { 0 }

Profile ID: LFWR-SCP-O-429352