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On the regularity of very weak minima*

Published online by Cambridge University Press:  14 November 2011

Daniela Giachetti ,
Francesco Leonetti  and
Rosanna Schianchi
Daniela Giachetti
Affiliation:
Dipartimento di Metodie Modelli Matematici, Università di Roma “La Sapienza”, Via Scarpa 10, 00161 Roma, Italy
Francesco Leonetti
Affiliation:
Dipartimento di Matematica, Università di L'Aquila, 67100 L'Aquila, Italy
Rosanna Schianchi
Affiliation:
Dipartimento di Matematica, Università di L'Aquila, 67100 L'Aquila, Italy
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Extract

We consider very weak minimisers u of variational integrals ∫ F(x, Du(x)) dx and very weak solutions u of nonlinear elliptic systems div A(x, u, Du) = 0; we prove higher integrability for the gradient Du without any homogeneity on ξ→A(x,u,ξ) thus improving on a result by Iwaniec and Sbordone.

Type
Research Article
Information
Proceedings of the Royal Society of Edinburgh Section A: Mathematics , Volume 126 , Issue 2 , 1996 , pp. 287 - 296
Copyright
Copyright © Royal Society of Edinburgh 1996

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