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        Partial Differential Equations, Convexity and Weak Lower Semi-Continuity

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        KoenVernooijBachelorThesis.pdf (593.5Kb)
        Publication date
        2015
        Author
        Vernooij, K.A.
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        Summary
        This thesis is concerned with the calculus of variations on bounded domains. The critical points of a functional I corresponding to a Lagragian function L are the solutions of the Euler-Lagrange equation. This equation is a partial differential equation. I will prove in the main theorem that there exists a minimizer to the functional I under certain conditions on L. These conditions are partial convexity and coercivity. Partial convexity is convexity in a part of the variable of L and coercivity is a bound from below of L with respect to another function. In the last subsection I will provide a motivation for the hypothesis of this theorem.
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        https://studenttheses.uu.nl/handle/20.500.12932/23506
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