no. 1
Lipschitz regularity for some asymptotically convex problems
ESAIM: Control, Optimisation and Calculus of Variations, Tome 17 (2011) no. 1, pp. 178-189.

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

DOI : 10.1051/cocv/2009046
Classification : 35B65, 35J70
Mots clés : local minimizers, decay estimates, asymptotic behaviour 
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     author = {Diening, Lars and Stroffolini, Bianca and Verde, Anna},
     title = {Lipschitz regularity for some asymptotically convex problems},
     journal = {ESAIM: Control, Optimisation and Calculus of Variations},
     pages = {178--189},
     publisher = {EDP-Sciences},
     volume = {17},
     number = {1},
     year = {2011},
     doi = {10.1051/cocv/2009046},
     mrnumber = {2775192},
     zbl = {1231.35031},
     language = {en},
     url = {http://www.numdam.org/articles/10.1051/cocv/2009046/}
}
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Diening, Lars; Stroffolini, Bianca; Verde, Anna. Lipschitz regularity for some asymptotically convex problems. ESAIM: Control, Optimisation and Calculus of Variations, Tome 17 (2011) no. 1, pp. 178-189. doi : 10.1051/cocv/2009046. http://www.numdam.org/articles/10.1051/cocv/2009046/

[1] E. Acerbi and N. Fusco, Regularity for minimizers of non-quadratic functionals: the case 1<p<2. J. Math. Anal. Appl. 140 (1989) 115-135. | MR | Zbl

[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. | MR | Zbl

[3] E. Acerbi and G. Mingione, Regularity results for stationary electro-rheological fluids. Arch. Ration. Mech. Anal. 164 (2002) 213-259. | MR | Zbl

[4] M. Chipot and L.C. Evans, Linearization at infinity and Lipschitz estimate for certain problems in the Calculus of Variations. Proc. Roy. Soc. Edinburgh Sect. A 102 (1986) 291-303. | MR | Zbl

[5] 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. | MR | Zbl

[6] A. Cianchi and N. Fusco, Gradient regularity for minimizers under general growth conditions. J. Reine Angew. Math. 507 (1999) 15-36. | MR | Zbl

[7] M. Cupini, M. Guidorzi and E. Mascolo, Regularity of minimizers of vectorial integrals with p-q growth. Nonlinear Anal. 54 (2003) 591-616. | MR | Zbl

[8] L. Diening and F. Ettwein, Fractional estimates for non-differentiable elliptic systems with general growth. Forum Math. 20 (2008) 523-556. | MR | Zbl

[9] L. Diening, B. Stroffolini and A. Verde, Regularity of functionals with ϕ-growth. Manuscripta Math. 129 (2009) 449-481. | MR | Zbl

[10] G. Dolzmann and J. Kristensen, Higher integrability of minimizing Young measures. Calc. Var. Partial Differ. Equ. 22 (2005) 283-301. | MR | Zbl

[11] M. Foss, Global regularity for almost minimizers of nonconvex variational problems. Ann. Mat. Pura Appl. 187 (2008) 263-321. | MR | Zbl

[12] M. Foss, A. Passarelli Di Napoli and A. Verde, Global Morrey regularity results for asymptotically convex variational problems. Forum Math. 20 (2008) 921-953. | MR | Zbl

[13] M. Fuchs, Regularity for a class of variational integrals motivated by nonlinear elasticity. Asymptotic Anal. 9 (1994) 23-38. | MR | Zbl

[14] M. Fuchs, Lipschitz regularity for certain problems from relaxation. Asymptotic Anal. 12 (1996) 145-151. | MR | Zbl

[15] M. Giaquinta and G. Modica, Remarks on the regularity of the minimizers of certain degenerate functionals. Manuscripta Math. 57 (1986) 55-99. | MR | Zbl

[16] J. Kristensen and A. Taheri, Partial regularity of strong local minimizers in the multi-dimensional calculus of variations. Arch. Ration. Mech. Anal. 170 (2003) 63-89. | MR | Zbl

[17] C. Leone, A. Passarelli Di Napoli and A. Verde, Lipschitz regularity for some asymptotically subquadratic problems. Nonlinear Anal. 67 (2007) 1532-1539. | MR | Zbl

[18] P. Marcellini, Regularity of minimizers of integrals of the calculus of variations with non standard growth conditions. Arch. Ration. Mech. Anal. 105 (1989) 267-284. | MR | Zbl

[19] P. Marcellini, Regularity and existence of solutions of elliptic equations with p,q-growth conditions. J. Diff. Eq. 90 (1991) 1-30. | MR | Zbl

[20] P. Marcellini, Everywhere regularity for a class of elliptic systems without growth conditions. Ann. Scuola Norm. Pisa 23 (1996) 1-25. | Numdam | MR | Zbl

[21] P. Marcellini and G. Papi, Nonlinear elliptic systems with general growth. J. Diff. Eq. 221 (2006) 412-443. | MR

[22] G.R. Mingione, Regularity of minima: An invitation to the dark side of the calculus of variations. Appl. Math. 51 (2006) 355-426. | MR | Zbl

[23] A. Passarelli Di Napoli and A. Verde, A regularity result for asymptotically convex problems with lower order terms. J. Convex Anal. 15 (2008) 131-148. | MR | Zbl

[24] J.P. Raymond, Lipschitz regularity of solutions of some asymptotically convex problems Proc. Roy. Soc. Edinburgh Sect. A 117 (1991) 59-73. | MR | Zbl

[25] 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. | MR | Zbl

[26] K. Uhlenbeck, Regularity for a class of nonlinear elliptic systems. Acta Math. 138 (1977) 219-240. | MR | Zbl

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