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Variational Methods for Nonlinear Partial Differential Equations

Electronic Theses and Dissertations

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abstract
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.
subject
free-boundary problems
lower semicontinuity
partial differential equations
Sobolev spaces
variational analysis
weak topology
contributor
Tello, Carlos A. (author)
Raynor, Sarah (committee chair)
Robinson, Stephen B (committee member)
Carmichael, Richard D (committee member)
date
2011-02-16T21:42:15Z (accessioned)
2011-02-16T21:42:15Z (available)
2010 (issued)
degree
Mathematics (discipline)
identifier
http://hdl.handle.net/10339/30397 (uri)
language
en (iso)
publisher
Wake Forest University
title
Variational Methods for Nonlinear Partial Differential Equations
type
Thesis

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