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

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abstract
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.
subject
Analysis
Free Boundary Problem
Partial Differential Equations
contributor
Moon, Gary Alan (author)
Raynor, Sarah G. (committee chair)
Robinson, Stephen (committee member)
Parsley, Jason (committee member)
Rivas, Mauricio (committee member)
date
2016-05-21T08:35:53Z (accessioned)
2017-05-20T08:30:09Z (available)
2016 (issued)
degree
Mathematics (discipline)
embargo
2017-05-20 (terms)
identifier
http://hdl.handle.net/10339/59325 (uri)
language
en (iso)
publisher
Wake Forest University
title
Neumann Solutions to a Two-Phase Elliptic Free Boundary Problem in R^2
type
Thesis

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