Dans cet article, les auteurs étudient la régularité sur la frontière ∂Ω d'un ouvert borné des minimiseurs u des fonctionnelles d'énergie du type suivant :
The paper is devoted to the study of the regularity on the boundary ∂Ω of a bounded open set for minimizers u for -energy functionals of the following type
Mots clés : $ p(x)$-growth, Minimizer, Boundary regularity
@article{AIHPC_2016__33_2_451_0, author = {Ragusa, Maria Alessandra and Tachikawa, Atsushi}, title = {Boundary regularity of minimizers of \protect\emph{p}(\protect\emph{x})-energy functionals}, journal = {Annales de l'I.H.P. Analyse non lin\'eaire}, pages = {451--476}, publisher = {Elsevier}, volume = {33}, number = {2}, year = {2016}, doi = {10.1016/j.anihpc.2014.11.003}, zbl = {1333.49052}, mrnumber = {3465382}, language = {en}, url = {http://www.numdam.org/articles/10.1016/j.anihpc.2014.11.003/} }
TY - JOUR AU - Ragusa, Maria Alessandra AU - Tachikawa, Atsushi TI - Boundary regularity of minimizers of p(x)-energy functionals JO - Annales de l'I.H.P. Analyse non linéaire PY - 2016 SP - 451 EP - 476 VL - 33 IS - 2 PB - Elsevier UR - http://www.numdam.org/articles/10.1016/j.anihpc.2014.11.003/ DO - 10.1016/j.anihpc.2014.11.003 LA - en ID - AIHPC_2016__33_2_451_0 ER -
%0 Journal Article %A Ragusa, Maria Alessandra %A Tachikawa, Atsushi %T Boundary regularity of minimizers of p(x)-energy functionals %J Annales de l'I.H.P. Analyse non linéaire %D 2016 %P 451-476 %V 33 %N 2 %I Elsevier %U http://www.numdam.org/articles/10.1016/j.anihpc.2014.11.003/ %R 10.1016/j.anihpc.2014.11.003 %G en %F AIHPC_2016__33_2_451_0
Ragusa, Maria Alessandra; Tachikawa, Atsushi. Boundary regularity of minimizers of p(x)-energy functionals. Annales de l'I.H.P. Analyse non linéaire, Tome 33 (2016) no. 2, pp. 451-476. doi : 10.1016/j.anihpc.2014.11.003. http://www.numdam.org/articles/10.1016/j.anihpc.2014.11.003/
[1] Regularity results for a class of functionals with non-standard growth, Arch. Ration. Mech. Anal., Volume 156 (2001) no. 2, pp. 121–140 | DOI | MR | Zbl
[2] Regularity results for a class of quasiconvex functionals with nonstandard growth, Ann. Sc. Norm. Super. Pisa Cl. Sci. (4), Volume 30 (2001) no. 2, pp. 311–339 | Numdam | MR | Zbl
[3] Regularity results for stationary electro-rheological fluids, Arch. Ration. Mech. Anal., Volume 164 (2002) no. 3, pp. 213–259 | DOI | MR | Zbl
[4] Hölder continuity of the gradient of -harmonic mappings, C. R. Acad. Sci. Paris Sér. I Math., Volume 328 (1999) no. 4, pp. 363–368 | DOI | MR | Zbl
[5] Integral representation and Γ-convergence of variational integrals with -growth, ESAIM Control Optim. Calc. Var., Volume 7 (2002), pp. 495–519 (electronic) | DOI | Numdam | MR | Zbl
[6] Partial and full boundary regularity for minimizers of functionals with nonquadratic growth, J. Convex Anal., Volume 11 (2004) no. 2, pp. 437–476 | MR | Zbl
[7] Hölder continuity results for a class of functionals with non-standard growth, Boll. Unione Mat. Ital., Sez. B, Artic. Ric. Mat. (8), Volume 7 (2004) no. 1, pp. 129–157 | MR | Zbl
[8] Calderón–Zygmund type estimates for a class of obstacle problems with growth, J. Math. Anal. Appl., Volume 372 (2010) no. 1, pp. 140–161 | DOI | MR | Zbl
[9] A Hölder continuity result for a class of obstacle problems under non standard growth conditions, Math. Nachr., Volume 284 (2011) no. 11–12, pp. 1404–1434 | MR | Zbl
[10] An Introduction to the Regularity Theory for Elliptic Systems, Harmonic Maps and Minimal Graphs, Lecture Notes. Scuola Normale Superiore di Pisa (New Series), vol. 11, Edizioni della Normale, Pisa, 2012 | MR | Zbl
[11] Direct Methods in the Calculus of Variations, World Scientific Publishing Co. Inc., River Edge, NJ, 2003 | DOI | MR | Zbl
[12] Boundary regularity for minima of certain quadratic functionals, Math. Ann., Volume 262 (1983) no. 4, pp. 549–561 | DOI | MR | Zbl
[13] Regularity of minimizers of integrals of the calculus of variations with nonstandard growth conditions, Arch. Ration. Mech. Anal., Volume 105 (1989) no. 3, pp. 267–284 | DOI | MR | Zbl
[14] On interior regularity of minimizers of -energy functionals, Nonlinear Anal., Volume 93 (2013), pp. 162–167 | DOI | MR | Zbl
[15] Partial regularity of -harmonic maps, Trans. Am. Math. Soc., Volume 365 (2013) no. 6, pp. 3329–3353 | DOI | MR | Zbl
[16] On the singular set of minimizers of -energies, Calc. Var. Partial Differ. Equ., Volume 50 (2014) no. 1–2, pp. 145–169 | MR | Zbl
[17] On Lavrentiev's phenomenon, Russ. J. Math. Phys., Volume 3 (1995) no. 2, pp. 249–269 | MR | Zbl
[18] On some variational problems, Russ. J. Math. Phys., Volume 5 (1997), pp. 105–116 | MR | Zbl
Cité par Sources :