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Continuous Extension of Functionals over W^{1,1}

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In the Calculus of Variations, the Direct Method is employed to prove the existence of global minimisers for functionals defined on Sobolev Spaces W^{1,p} for p>1. Due to a lack of reflexivity, the situation for p=1 is much harder. In this talk, I will start by giving a description of the Direct Method as it is traditionally used and an explanation of the problems encountered for the case p=1. I will then present recent results explaining how these problems can be overcome, obtained in collaboration with Filip Rindler.

This talk is part of the Cambridge Analysts' Knowledge Exchange series.

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