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We establish a local Lipschitz regularity result for local minimizers of asymptotically convex variational integrals.
Acerbi, E. and Fusco, N., Regularity for minimizers of non-quadratic functionals: the case 1<p<2. J. Math. Anal. Appl.140 (1989) 115–135.
CrossRef
[2]
E. Acerbi and G. Mingione, Regularity results for a class of functionals with non-standard growth. Arch. Ration. Mech. Anal. 156 (2001) 121–140.
[3]
Acerbi, E. and Mingione, G., Regularity results for stationary electro-rheological fluids. Arch. Ration. Mech. Anal.164 (2002) 213–259.
CrossRef
[4]
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. A102 (1986) 291–303.
CrossRef
[5]
A. Cianchi, Some results in the theory of Orlicz spaces and applications to variational problems, in Nonlinear Analysis, Function Spaces and Applications6, Acad. Sci. Czech Repub., Prague, Czech Republic (1999) 50–92.
[6]
Cianchi, A. and Fusco, N., Gradient regularity for minimizers under general growth conditions. J. Reine Angew. Math.507 (1999) 15–36.
[7]
Cupini, M., Guidorzi, M. and Mascolo, E., Regularity of minimizers of vectorial integrals with p-q growth. Nonlinear Anal.54 (2003) 591–616.
CrossRef
[8]
Diening, L. and Ettwein, F., Fractional estimates for non-differentiable elliptic systems with general growth. Forum Math.20 (2008) 523–556.
CrossRef
[9]
Diening, L., Stroffolini, B. and Verde, A., Regularity of functionals with ϕ-growth. Manuscripta Math.129 (2009) 449–481.
CrossRef
[10]
Dolzmann, G. and Kristensen, J., Higher integrability of minimizing Young measures. Calc. Var. Partial Differ. Equ.22 (2005) 283–301.
CrossRef
[11]
Foss, M., Global regularity for almost minimizers of nonconvex variational problems. Ann. Mat. Pura Appl.187 (2008) 263–321.
CrossRef
[12]
Foss, M., Passarelli di, A. Napoli and A. Verde, Global Morrey regularity results for asymptotically convex variational problems. Forum Math.20 (2008) 921–953.
CrossRef
[13]
Fuchs, M., Regularity for a class of variational integrals motivated by nonlinear elasticity. Asymptotic Anal.9 (1994) 23–38.
[14]
Fuchs, M., Lipschitz regularity for certain problems from relaxation. Asymptotic Anal.12 (1996) 145–151.
[15]
Giaquinta, M. and Modica, G., Remarks on the regularity of the minimizers of certain degenerate functionals. Manuscripta Math.57 (1986) 55–99.
CrossRef
[16]
Kristensen, J. and Taheri, A., Partial regularity of strong local minimizers in the multi-dimensional calculus of variations. Arch. Ration. Mech. Anal.170 (2003) 63–89.
CrossRef
[17]
Leone, C., Passarelli di, A. Napoli and A. Verde, Lipschitz regularity for some asymptotically subquadratic problems. Nonlinear Anal.67 (2007) 1532–1539.
CrossRef
[18]
Marcellini, P., Regularity of minimizers of integrals of the calculus of variations with non standard growth conditions. Arch. Ration. Mech. Anal.105 (1989) 267–284.
CrossRef
[19]
Marcellini, P., Regularity and existence of solutions of elliptic equations with p,q-growth conditions. J. Diff. Eq.90 (1991) 1–30.
CrossRef
[20]
Marcellini, P., Everywhere regularity for a class of elliptic systems without growth conditions. Ann. Scuola Norm. Pisa23 (1996) 1–25.
[21]
Marcellini, P. and Papi, G., Nonlinear elliptic systems with general growth. J. Diff. Eq.221 (2006) 412–443.
CrossRef
[22]
Mingione, G.R., Regularity of minima: An invitation to the dark side of the calculus of variations. Appl. Math.51 (2006) 355–426.
CrossRef
[23]
Passarelli di, A. Napoli and A. Verde, A regularity result for asymptotically convex problems with lower order terms. J. Convex Anal.15 (2008) 131–148.
[24]
J.P. Raymond, Lipschitz regularity of solutions of some asymptotically convex problems Proc. Roy. Soc. Edinburgh Sect. A117 (1991) 59–73.
[25]
M. Ružička and L. Diening, Non-Newtonian fluids and function spaces, in Nonlinear Analysis, Function Spaces and Applications8, Acad. Sci. Czech Repub., Prague, Czech Republic (2007) 95–143.
[26]
Uhlenbeck, K., Regularity for a class of nonlinear elliptic systems. Acta Math.138 (1977) 219–240.
CrossRef