2026-09-20T22:42:11Zhttps://wakespace.lib.wfu.edu/server/oai/request

oai:null:10339/593252026-09-18T11:54:49Zcom_10339_14934col_10339_38132

Moon, Gary Alan 2016-05-21T08:35:53Z 2017-05-20T08:30:09Z 2016 https://wakespace.lib.wfu.edu/handle/10339/59325 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. en Wake Forest University Analysis Free Boundary Problem Partial Differential Equations Neumann Solutions to a Two-Phase Elliptic Free Boundary Problem in R^2 Thesis Raynor, Sarah G. Robinson, Stephen Parsley, Jason Rivas, Mauricio Mathematics 2017-05-20 open.access