Boundary Regularity in Variational Problems |
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Authors: | Jan Kristensen Giuseppe Mingione |
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Institution: | 1. Mathematical Institute, University of Oxford, 24-29 St. Giles’, Oxford, OX1 3LB, UK 2. Dipartimento di Matematica, Università di Parma, Viale Usberti 53/a, 43100, Parma, taly
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Abstract: | We prove that, if ${u : \Omega \subset \mathbb{R}^n \to \mathbb{R}^N}We prove that, if
u : W ì \mathbbRn ? \mathbbRN{u : \Omega \subset \mathbb{R}^n \to \mathbb{R}^N} is a solution to the Dirichlet variational problem
minwòW F(x, w, Dw) dx subject to w o u0 on ?W,\mathop {\rm min}\limits_{w}\int_{\Omega} F(x, w, Dw)\,{\rm d}x \quad {\rm subject \, to} \quad w \equiv u_0 {\rm on}\partial \Omega, |
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