Neumann Solutions to a Two-Phase Elliptic Free Boundary Problem in R^2

This thesis concerns the problem of minimizing a particular energy functional over an appropriate class of admissible functions on a bounded, convex domain in two-dimensional Euclidean space. We require admissible functions to satisfy Dirichlet boundary conditions on a portion of the fixed boundary with positive one-dimensional Hausdorff measure and Neumann boundary conditions on the rest of the fixed boundary. In this thesis we consider the behavior of minimizers in a neighborhood of some point on the Neumann fixed boundary. The primary result is that minimizers are Lipschitz continuous up to the Neumann fixed boundary.

Grantor dc:publisher

Wake Forest University

Year dc:date.issued

2016

Author dc:creator

• Moon, Gary Alan

• Analysis

Language dc:language.iso

en

Handle dc:identifier.uri

http://hdl.handle.net/10339/59325

OAI identifier oai:identifier

oai:wakespace.lib.wfu.edu:10339/59325