Hostname: page-component-586b7cd67f-2brh9 Total loading time: 0 Render date: 2024-12-03T19:18:33.079Z Has data issue: false hasContentIssue false
  • English
  • Français

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
Get access Rights & Permissions [Opens in a new window]

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

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

References

1Acerbi, E. and Fusco, N.. A transmission problem in the calculus of variations Cal. Var. 2 (1994), 1–16.CrossRefGoogle Scholar
2Giaquinta, M.. Multiple integrals in the calculus of variations and nonlinear elliptic systems (Princeton, 1983), Annals of Matbemics Studies. 105.Google Scholar
3Giaquinta, M. and Giusti, E.. On the regularity of the minima of variational integrals. Acta Math. 148 (1982), 31–46.CrossRefGoogle Scholar
4Giaquinta, M. and Modica, G.. Regularity results for some classes of higher order nonlinear elliptic systems. J. Reine Angev. Math. 311/312 (1979), 145–69.Google Scholar
5Iwaniec, T.. p-harmonic tensors and quasiregular mappings. Ann. Math. 136 (1992), 589–624.CrossRefGoogle Scholar
6Iwaniec, T. and Sbordone, C.. Weak minima of variational integrals. J. Reine Angew. Math. 454 (1994), 143–61.Google Scholar
7Lewis, J.. On very weak solutions of certain elliptic systems. Comm. Partial Differential Equations 18 (1993), 1515–37.CrossRefGoogle Scholar
8Li, C., Mclntosh, A. and Zhang, K.. Higher integrability and reverse Hölder inequalities (Preprint).Google Scholar
9Meyers, N.. An Lp-estimate for the gradient of solutions of second order elliptic divergence equations. Ann. Scuola Norm. Sup. Pisa 17 (1963), 189–206.Google Scholar
10Meyers, N. and Elcrat, A.. Some results on regularity for solutions of nonlinear ellipticsystems and quasi regular functions. Duke Math. J. 42 (1975). 121–36.CrossRefGoogle Scholar