We prove Lipschitz continuity for local minimizers of integral functionals of the Calculus of Variations in the vectorial case, where the energy density depends explicitly on the space variables and has general growth with respect to the gradient. One of the models is
Classification : 49N60, 35J50
Mots clés : minimizers, regularity, nonstandard growth, exponential growth
@article{COCV_2003__9__399_0, author = {Mascolo, Elvira and Migliorini, Anna Paola}, title = {Everywhere regularity for vectorial functionals with general growth}, journal = {ESAIM: Control, Optimisation and Calculus of Variations}, pages = {399--418}, publisher = {EDP-Sciences}, volume = {9}, year = {2003}, doi = {10.1051/cocv:2003019}, zbl = {1066.49023}, mrnumber = {1988669}, language = {en}, url = {http://www.numdam.org/articles/10.1051/cocv:2003019/} }
TY - JOUR AU - Mascolo, Elvira AU - Migliorini, Anna Paola TI - Everywhere regularity for vectorial functionals with general growth JO - ESAIM: Control, Optimisation and Calculus of Variations PY - 2003 DA - 2003/// SP - 399 EP - 418 VL - 9 PB - EDP-Sciences UR - http://www.numdam.org/articles/10.1051/cocv:2003019/ UR - https://zbmath.org/?q=an%3A1066.49023 UR - https://www.ams.org/mathscinet-getitem?mr=1988669 UR - https://doi.org/10.1051/cocv:2003019 DO - 10.1051/cocv:2003019 LA - en ID - COCV_2003__9__399_0 ER -
Mascolo, Elvira; Migliorini, Anna Paola. Everywhere regularity for vectorial functionals with general growth. ESAIM: Control, Optimisation and Calculus of Variations, Tome 9 (2003), pp. 399-418. doi : 10.1051/cocv:2003019. http://www.numdam.org/articles/10.1051/cocv:2003019/
[1] The mathematical theory of diffusion and reaction of permeable catalysts. Clarendon Press, Oxford (1975). | Zbl 0315.76051
,[2] Regularity for minimizers of non-quadratic functionals: The case . J. Math. Anal. Appl. 140 (1989) 115-135. | MR 997847 | Zbl 0686.49004
and ,[3] Regularity results for a class of functionals with nonstandard growth. Arch. Rational Mech. Anal. 156 (2001) 121-140. | MR 1814973 | Zbl 0984.49020
and ,[4] Regularity results for quasiconvex functionals with nonstandard growth. Ann. Scuola Norm. Sup. Pisa 30 (2001). | Numdam | MR 1895714 | Zbl 1027.49031
and ,[5] Hölder continuity of minimizers of functionals with variable growth exponent. Manuscripta Math. 93 (1997) 283-299. | MR 1457729 | Zbl 0878.49010
and ,[6] Hölder continuity of the gradient of -harmonic mappings. C. R. Acad. Sci. Paris 328 (1999) 363-368. | MR 1675954 | Zbl 0920.49020
and ,[7] Local boundedness for minima of functionals with non standard growth conditions. Rend. Mat. 18 (1998) 305-326. | Zbl 0917.49010
, and ,[8] -estimates for a class of nonlinear elliptic systems with non standard growth. Atti Sem. Mat. Fis. Univ. Modena (to appear).
and ,[9] Everywhere regularity for a class of vectorial functionals under subquadratic general growth, Preprint. Dipartimento di Matematica “U. Dini”, University of Florence.
, and ,[10] Multiple integrals in the calculus of variations and non linear elliptic systems. Princeton Univ. Press, Princeton NJ, Ann. Math. Stud. 105 (1983). | MR 717034 | Zbl 0516.49003
,[11] Remarks on the regularity of the minimizers of certain degenerate functionals. Manuscripta Math. 57 (1986) 55-99. | MR 866406 | Zbl 0607.49003
and ,[12] Metodi diretti nel calcolo delle variazioni. UMI, Bologna (1994). | MR 1707291 | Zbl 0942.49002
,[13] Regularity and existence of solutions of elliptic equations with ()-growth conditions. J. Differential Equations 90 (1991) 1-30. | MR 1094446 | Zbl 0724.35043
,[14] Regularity for elliptic equations with general growth conditions. J. Differential Equations 105 (1993) 296-333. | MR 1240398 | Zbl 0812.35042
,[15] Everywhere regularity for a class of elliptic systems without growth conditions. Ann. Scuola Norm. Sup. Pisa 23 (1996) 1-25. | Numdam | MR 1401415 | Zbl 0922.35031
,[16] Continuity of certain Nemitsky operators on Sobolev spaces and chain rule. J. Anal. Math. 28 (1975) 303-334. | MR 482444 | Zbl 0328.46028
and ,[17] Local boundedness of integrals of Calculus of Variations. Ann. Mat. Pura Appl. 167 (1994) 323-339. | MR 1313560 | Zbl 0819.49023
and ,[18] Everywhere regularity for a class of elliptic systems with , growth conditions. Rend. Istit. Mat. Univ. Trieste XXXI (1999) 203-234. | MR 1763252 | Zbl 0956.35042
,[19] Everywhere regularity for a class of elliptic systems with general growth conditions, Ph.D. Thesis. University of Florence, Italy (2000).
,[20] A two dimensional Dirichlet problem with an exponential nonlinearity. SIAM J. Math. Anal. 14 5 (1983) 719-735. | Zbl 0543.35036
,[21] Flow of shear dependent electrorheological fluids. C. R. Acad. Sci. Paris 329 (1999) 393-398. | MR 1710119 | Zbl 0954.76097
,[22] On the modeling of electrorheological materials. Mech. Res. Commun. 23 (1996) 401-407. | Zbl 0890.76007
and ,[23] Regularity for a class of non-linear elliptic systems. Acta Math. 138 (1977) 219-240. | MR 474389 | Zbl 0372.35030
,[24] On Lavrentiev phenomenon. Russian J. Math. Phys. 3 (1995) 249-269. | MR 1350506 | Zbl 0910.49020
,Cité par Sources :