J Austral Math Soc Ser A 57 pp158--169, 1994.

Partial Regularity and Everywhere Continuity for a Model Problem from Non-Linear Elasticity

Nicola Fusco and John E. Hutchinson

Abstract

We prove a new energy or Caccioppoli type estimate for minimisers of the model functional f_W |Du|² + (det Du)², where W Ì R² and u : W® R². We apply this to establish C^¥ regularity for minimisers except on a closed set of measure zero. We also prove a maximm principle and use this to establish everywhere continuity of minimisers.

1991 AMS Subject Classification: 35J50, 35J60, 73C50

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Authors

Nicola Fusco

Dipatimento di Matematica "R. Cappioppoli", Universita di Napoli--Monte S. Angelo, Edificio T, via Cintia, 80100 Napoli, Italy.

John E. Hutchinson

Department of Mathematics, School of Mathematical Sciences, Australian National University, GPO Box 4, Canberra ACT 0200, Australia.