Neumann Solutions to a Two-Phase Elliptic Free Boundary Problem in R^2
Electronic Theses and Dissertations
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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
- 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