Hostname: page-component-7c8c6479df-r7xzm Total loading time: 0 Render date: 2024-03-29T07:49:23.445Z Has data issue: false hasContentIssue false

Lipschitz regularity of solutions of some asymptotically convex problems

Published online by Cambridge University Press:  14 November 2011

Jean-Pierre Raymond
Affiliation:
Université Paul Sabatier, Laboratoire d'Analyse Numérique, 118 Route de Narbonne, 31062 Toulouse Cedex, France

Synopsis

We prove local Lipschitz regularity for minimisers of integral functionals of the form J(u) = ∫Ω{f(Du(x)) + g(x, u(x))} dx, where the integrand f is not convex but satisfies some asymptotic convexity assumption.

Type
Research Article
Copyright
Copyright © Royal Society of Edinburgh 1991

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

1Adams, R. A.. Sobolev Spaces (New York: Academic Press, 1975).Google Scholar
2Acerbi, E. and Fusco, N.. Semicontinuity problems in the calculus of variations. Arch. Rational Mech. Anal. 86 (1984), 125145.CrossRefGoogle Scholar
3Ball, J. M.. Convexity conditions and existence theorems in nonlinear elasticity. Arch. Rational Mech. Anal. 63 (1977), 337403.CrossRefGoogle Scholar
4Chipot, M. and Evans, L. C.. Linearisation at infinity and Lipschitz estimates for certain problems in the calculus of variations. Proc. Roy. Soc. Edinburgh Sect. A 102 (1986) 291303.CrossRefGoogle Scholar
5Giaquinta, M.. Multiple integrals in the calculus of variations and nonlinear elliptic systems. (Princeton: Princeton University Press, Ann. of Math. Stud. 105, 1983).Google Scholar
6Giaquinta, M. and Modica, G.. Remarks on the regularity of the minimizers of certain degenerate functionals. Manuscripta Math. 57, (1986), 5599.CrossRefGoogle Scholar
7R, Kohn and Strang, G.. Optimal Design and Relaxation of Variational Problems I, II, III. Comm. Pure Appl. Math. 39 (1986) 113-137; 139-182; 183232.Google Scholar
8Stampacchia, G.. On some regular multiple integral problems in the calculus of variations. Comm. Pure Appl. Math. 16 (1963), 383421.CrossRefGoogle Scholar
9Tolksdorf, P.. Everywhere regularity for some quasilinear systems with a lack of ellipticity. Ann. Mat. Pura. Appl. 134 (1983) 241266.CrossRefGoogle Scholar
10Uhlenbeck, K.. Regularity for a class of nonlinear elliptic systems. Ada Math. 138 (1977), 219240.Google Scholar