Regularity of solutions of a degenerate elliptic variational problem
摘要：
We prove regularity of minimizers of the functional F(s,{\mathbf{ }}u) = \int\limits_\Omega {\left( {\kappa \left| {abla s} ight|^2 + s^2 \left| {abla u} ight|^2 + \Psi (s)} ight)} {\mathbf{ }}dx F(s,{\mathbf{ }}u) = \int\limits_\Omega {\left( {\kappa \left| {abla s} ight|^2 + s^2 \left| {abla u} ight|^2 + \Psi (s)} ight)} {\mathbf{ }}dx recently suggested by Ericksen [10] for the statics of nematic liquid crystals. We show that, given locally minimizing pairs ( s, u ), s has a continuous representative, and s, u are smooth outside the set { s =0}. The proof relies upon higher integrability estimates, monotonicity, and decay lemmas.
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DOI：
10.1007/bf02568766
被引量：
年份：
1990
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