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Partial regularity and everywhere continuity for a model problem from non-linear elasticity

Part of: Elliptic equations and systems

Published online by Cambridge University Press:  09 April 2009

Nicola Fusco  and
John E. Hutchinson
Nicola Fusco
Affiliation:
Dipartmento di Mathematica “R. Caccioppoli”, Università di Napoli—Monte S. Angelo, Edificio T, via Cintia, 80100 Napoli, Italy
John E. Hutchinson
Affiliation:
Department of Mathematics, School of Mathematical Sciences, Australian National University, GPO Box 4, Canberra ACT 0200, Australia
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Abstract

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We prove a new energy or Caccioppoli type estimate for minimisers of the model functional ∫Ω|Du|2 + (det Du)2, where Ω ⊂ 2 and u: Ω → 2. We apply this to establish C∞ regularity for minimisers except on a closed set of measure zero. We also prove a maximum principle and use this to establish everywhere continuity of minimisers.

Keywords

nonlinear elasticitypartial regularityelliptic systemspolyconvexquasiconvexmaximum principle.

MSC classification

Secondary: 35J50: Variational methods for elliptic systems
Type
Research Article
Information
Journal of the Australian Mathematical Society , Volume 57 , Issue 2 , October 1994 , pp. 158 - 169
Copyright
Copyright © Australian Mathematical Society 1994

References

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