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Partial regularity and everywhere continuity for a model problem from non-linear elasticity
- Part of
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- Journal:
- Journal of the Australian Mathematical Society. Series A. Pure Mathematics and Statistics / Volume 57 / Issue 2 / October 1994
- Published online by Cambridge University Press:
- 09 April 2009, pp. 158-169
- Print publication:
- October 1994
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- Article
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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.
