Hostname: page-component-76fb5796d-vfjqv Total loading time: 0 Render date: 2024-04-26T13:03:03.223Z Has data issue: false hasContentIssue false

Lipschitz regularity for some asymptotically convexproblems*

Published online by Cambridge University Press:  04 December 2009

Lars Diening
Affiliation:
Institute of Mathematics, Eckerstr. 1, 79104 Freiburg, Germany. diening@mathematik.uni-freiburg.de
Bianca Stroffolini
Affiliation:
Dipartimento di Matematica, Università di Napoli, Federico II, Via Cintia, 80126 Napoli, Italy. bstroffo@unina.it; anverde@unina.it
Anna Verde
Affiliation:
Dipartimento di Matematica, Università di Napoli, Federico II, Via Cintia, 80126 Napoli, Italy. bstroffo@unina.it; anverde@unina.it
Get access

Abstract

We establish a local Lipschitz regularity result for local minimizers of asymptotically convex variational integrals.

Type
Research Article
Copyright
© EDP Sciences, SMAI, 2009

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

Acerbi, E. and Fusco, N., Regularity for minimizers of non-quadratic functionals: the case 1<p<2. J. Math. Anal. Appl. 140 (1989) 115135. CrossRef
E. Acerbi and G. Mingione, Regularity results for a class of functionals with non-standard growth. Arch. Ration. Mech. Anal. 156 (2001) 121–140.
Acerbi, E. and Mingione, G., Regularity results for stationary electro-rheological fluids. Arch. Ration. Mech. Anal. 164 (2002) 213259. CrossRef
Chipot, M. and Evans, L.C., Linearization at infinity and Lipschitz estimate for certain problems in the Calculus of Variations. Proc. Roy. Soc. Edinburgh Sect. A 102 (1986) 291303. CrossRef
A. Cianchi, Some results in the theory of Orlicz spaces and applications to variational problems, in Nonlinear Analysis, Function Spaces and Applications 6, Acad. Sci. Czech Repub., Prague, Czech Republic (1999) 50–92.
Cianchi, A. and Fusco, N., Gradient regularity for minimizers under general growth conditions. J. Reine Angew. Math. 507 (1999) 1536.
Cupini, M., Guidorzi, M. and Mascolo, E., Regularity of minimizers of vectorial integrals with p-q growth. Nonlinear Anal. 54 (2003) 591616. CrossRef
Diening, L. and Ettwein, F., Fractional estimates for non-differentiable elliptic systems with general growth. Forum Math. 20 (2008) 523556. CrossRef
Diening, L., Stroffolini, B. and Verde, A., Regularity of functionals with ϕ-growth. Manuscripta Math. 129 (2009) 449481. CrossRef
Dolzmann, G. and Kristensen, J., Higher integrability of minimizing Young measures. Calc. Var. Partial Differ. Equ. 22 (2005) 283301. CrossRef
Foss, M., Global regularity for almost minimizers of nonconvex variational problems. Ann. Mat. Pura Appl. 187 (2008) 263321. CrossRef
Foss, M., Passarelli di, A. Napoli and A. Verde, Global Morrey regularity results for asymptotically convex variational problems. Forum Math. 20 (2008) 921953. CrossRef
Fuchs, M., Regularity for a class of variational integrals motivated by nonlinear elasticity. Asymptotic Anal. 9 (1994) 2338.
Fuchs, M., Lipschitz regularity for certain problems from relaxation. Asymptotic Anal. 12 (1996) 145151.
Giaquinta, M. and Modica, G., Remarks on the regularity of the minimizers of certain degenerate functionals. Manuscripta Math. 57 (1986) 5599. CrossRef
Kristensen, J. and Taheri, A., Partial regularity of strong local minimizers in the multi-dimensional calculus of variations. Arch. Ration. Mech. Anal. 170 (2003) 6389. CrossRef
Leone, C., Passarelli di, A. Napoli and A. Verde, Lipschitz regularity for some asymptotically subquadratic problems. Nonlinear Anal. 67 (2007) 15321539. CrossRef
Marcellini, P., Regularity of minimizers of integrals of the calculus of variations with non standard growth conditions. Arch. Ration. Mech. Anal. 105 (1989) 267284. CrossRef
Marcellini, P., Regularity and existence of solutions of elliptic equations with p,q-growth conditions. J. Diff. Eq. 90 (1991) 130. CrossRef
Marcellini, P., Everywhere regularity for a class of elliptic systems without growth conditions. Ann. Scuola Norm. Pisa 23 (1996) 125.
Marcellini, P. and Papi, G., Nonlinear elliptic systems with general growth. J. Diff. Eq. 221 (2006) 412443. CrossRef
Mingione, G.R., Regularity of minima: An invitation to the dark side of the calculus of variations. Appl. Math. 51 (2006) 355426. CrossRef
Passarelli di, A. Napoli and A. Verde, A regularity result for asymptotically convex problems with lower order terms. J. Convex Anal. 15 (2008) 131148.
J.P. Raymond, Lipschitz regularity of solutions of some asymptotically convex problems Proc. Roy. Soc. Edinburgh Sect. A 117 (1991) 59–73.
M. Ružička and L. Diening, Non-Newtonian fluids and function spaces, in Nonlinear Analysis, Function Spaces and Applications 8, Acad. Sci. Czech Repub., Prague, Czech Republic (2007) 95–143.
Uhlenbeck, K., Regularity for a class of nonlinear elliptic systems. Acta Math. 138 (1977) 219240. CrossRef