2026-09-18T18:31:23Zhttps://wakespace.lib.wfu.edu/server/oai/request

oai:null:10339/303972026-04-21T20:59:10Zcom_10339_14934col_10339_38132

Tello, Carlos A. 2011-02-16T21:42:15Z 2011-02-16T21:42:15Z 2010 https://wakespace.lib.wfu.edu/handle/10339/30397 The objective of this work is to explain some basic aspects of variational methods for solving a class of nonlinear partial differential equations. First, relevant mathematical background of functional analysis and variational calculus is explained. One of the main results discussed is the existence theorem for minimizer of functionals for the case of fixed boundary problems. This theorem assumes coercivity and lower semicontinuity conditions of the functional and the energy functional is defined over subsets of Sobolev spaces. After that, the technical concepts associated to this theorem are implemented to study some specific free boundary problems. en Wake Forest University free-boundary problems lower semicontinuity partial differential equations Sobolev spaces variational analysis weak topology Variational Methods for Nonlinear Partial Differential Equations Thesis Raynor, Sarah Robinson, Stephen B Carmichael, Richard D Mathematics open.access