Lipschitz regularity for some asymptotically convex problems*
Lars Diening; Bianca Stroffolini; Anna Verde
ESAIM: Control, Optimisation and Calculus of Variations (2011)
- Volume: 17, Issue: 1, page 178-189
- ISSN: 1292-8119
Access Full Article
topAbstract
topHow to cite
topDiening, Lars, Stroffolini, Bianca, and Verde, Anna. "Lipschitz regularity for some asymptotically convex problems*." ESAIM: Control, Optimisation and Calculus of Variations 17.1 (2011): 178-189. <http://eudml.org/doc/197382>.
@article{Diening2011,
abstract = {
We establish a local Lipschitz regularity result for local
minimizers of asymptotically convex variational integrals.
},
author = {Diening, Lars, Stroffolini, Bianca, Verde, Anna},
journal = {ESAIM: Control, Optimisation and Calculus of Variations},
keywords = {Local minimizers; decay estimates; asymptotic
behaviour; Lipschitz regularity; local minimizer; variational integral},
language = {eng},
month = {2},
number = {1},
pages = {178-189},
publisher = {EDP Sciences},
title = {Lipschitz regularity for some asymptotically convex problems*},
url = {http://eudml.org/doc/197382},
volume = {17},
year = {2011},
}
TY - JOUR
AU - Diening, Lars
AU - Stroffolini, Bianca
AU - Verde, Anna
TI - Lipschitz regularity for some asymptotically convex problems*
JO - ESAIM: Control, Optimisation and Calculus of Variations
DA - 2011/2//
PB - EDP Sciences
VL - 17
IS - 1
SP - 178
EP - 189
AB -
We establish a local Lipschitz regularity result for local
minimizers of asymptotically convex variational integrals.
LA - eng
KW - Local minimizers; decay estimates; asymptotic
behaviour; Lipschitz regularity; local minimizer; variational integral
UR - http://eudml.org/doc/197382
ER -
References
top- 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.
- E. Acerbi and G. Mingione, Regularity results for a class of functionals with non-standard growth. Arch. Ration. Mech. Anal. 156 (2001) 121–140.
- E. Acerbi and G. Mingione, Regularity results for stationary electro-rheological fluids. Arch. Ration. Mech. Anal.164 (2002) 213–259.
- 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. A102 (1986) 291–303.
- 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.
- A. Cianchi and N. Fusco, Gradient regularity for minimizers under general growth conditions. J. Reine Angew. Math.507 (1999) 15–36.
- M. Cupini, M. Guidorzi and E. Mascolo, Regularity of minimizers of vectorial integrals with p-q growth. Nonlinear Anal.54 (2003) 591–616.
- L. Diening and F. Ettwein, Fractional estimates for non-differentiable elliptic systems with general growth. Forum Math.20 (2008) 523–556.
- L. Diening, B. Stroffolini and A. Verde, Regularity of functionals with ϕ-growth. Manuscripta Math.129 (2009) 449–481.
- G. Dolzmann and J. Kristensen, Higher integrability of minimizing Young measures. Calc. Var. Partial Differ. Equ.22 (2005) 283–301.
- M. Foss, Global regularity for almost minimizers of nonconvex variational problems. Ann. Mat. Pura Appl.187 (2008) 263–321.
- M. Foss, A. Passarelli di Napoli and A. Verde, Global Morrey regularity results for asymptotically convex variational problems. Forum Math.20 (2008) 921–953.
- M. Fuchs, Regularity for a class of variational integrals motivated by nonlinear elasticity. Asymptotic Anal.9 (1994) 23–38.
- M. Fuchs, Lipschitz regularity for certain problems from relaxation. Asymptotic Anal.12 (1996) 145–151.
- M. Giaquinta and G. Modica, Remarks on the regularity of the minimizers of certain degenerate functionals. Manuscripta Math.57 (1986) 55–99.
- 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.
- C. Leone, A. Passarelli di Napoli and A. Verde, Lipschitz regularity for some asymptotically subquadratic problems. Nonlinear Anal.67 (2007) 1532–1539.
- 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.
- P. Marcellini, Regularity and existence of solutions of elliptic equations with p,q-growth conditions. J. Diff. Eq.90 (1991) 1–30.
- P. Marcellini, Everywhere regularity for a class of elliptic systems without growth conditions. Ann. Scuola Norm. Pisa23 (1996) 1–25.
- P. Marcellini and G. Papi, Nonlinear elliptic systems with general growth. J. Diff. Eq.221 (2006) 412–443.
- G.R. Mingione, Regularity of minima: An invitation to the dark side of the calculus of variations. Appl. Math.51 (2006) 355–426.
- 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.
- J.P. Raymond, Lipschitz regularity of solutions of some asymptotically convex problems Proc. Roy. Soc. Edinburgh Sect. A117 (1991) 59–73.
- 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.
- K. Uhlenbeck, Regularity for a class of nonlinear elliptic systems. Acta Math.138 (1977) 219–240.
Citations in EuDML Documents
topNotesEmbed ?
topTo embed these notes on your page include the following JavaScript code on your page where you want the notes to appear.