The Mixed Problem in L ^p for Some Two-Dimensional Lipschitz Domains

Authors

Loredana Lanzani, University of Arkansas
Luca Capogna, University of ArkansasFollow
Russell M. Brown, University of Kentucky

Document Type

Article

Publication Date

9-1-2008

Publication Title

Mathematische Annalen

Abstract

We consider the mixed problem, {Δ u = 0 in Ω ∂u = f N on N u = fD on D in a class of Lipschitz graph domains in two dimensions with Lipschitz constant at most 1. We suppose the Dirichlet data, f D , has one derivative in L p (D) of the boundary and the Neumann data, f N , is in L p (N). We find a p 0 > 1 so that for p in an interval (1, p 0), we may find a unique solution to the mixed problem and the gradient of the solution lies in L p .

Volume

342

Issue

1

First Page

91

Last Page

124

DOI

10.1007/s00208-008-0223-6

ISSN

00255831

Comments

Peer reviewed accepted manuscript.

Recommended Citation

Lanzani, Loredana; Capogna, Luca; and Brown, Russell M., "The Mixed Problem in L ^p for Some Two-Dimensional Lipschitz Domains" (2008). Mathematics and Statistics: Faculty Publications, Smith College, Northampton, MA.
https://scholarworks.smith.edu/mth_facpubs/141