Gradient regularity for minimizers of functionals under p-q subquadratic growth
Leonetti, F. ; Mascolo, E. ; Siepe, F.
Bollettino dell'Unione Matematica Italiana, Tome 4-A (2001), p. 571-586 / Harvested from Biblioteca Digitale Italiana di Matematica
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Si prova la maggior sommabilità del gradiente dei minimi locali di funzionali integrali della forma ∫Ωf⁢D⁢u⁢d⁢x, dove f soddisfa l'ipotesi di crescita ξp-c1≤f⁢ξ≤c⁢1+ξq, con 1<p<q≤2. L'integrando f è C2 e D⁢D⁢f ha crescita p-2 dal basso e q-2 dall'alto.

Publié le : 2001-10-01
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     author = {F. Leonetti and E. Mascolo and F. Siepe},
     title = {Gradient regularity for minimizers of functionals under $p$-$q$ subquadratic growth},
     journal = {Bollettino dell'Unione Matematica Italiana},
     volume = {4-A},
     year = {2001},
     pages = {571-586},
     zbl = {1177.49057},
     mrnumber = {1859423},
     language = {en},
     url = {http://dml.mathdoc.fr/item/BUMI_2001_8_4B_3_571_0}
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Leonetti, F.; Mascolo, E.; Siepe, F. Gradient regularity for minimizers of functionals under $p$-$q$ subquadratic growth. Bollettino dell'Unione Matematica Italiana, Tome 4-A (2001) pp. 571-586. http://gdmltest.u-ga.fr/item/BUMI_2001_8_4B_3_571_0/

[A] Adams, R. A., Sobolev spaces, Academic Press, New York, 1975. | MR 450957 | Zbl 0314.46030

[AF] Acerbi, E.-Fusco, N., Regularity for minimizers of non-quadratic functionals. The case 1<p<2, Journ. of Math. Anal. and Applications, 140 (1989), 115-135. | MR 997847 | Zbl 0686.49004

[BL] Bhattacharya, T.-Leonetti, F., A new Poincaré inequality and its applications to the regularity of minimizers of integral functionals with nonstandard growth, Nonlinear Analysis TMA, vol. 17, 9 (1991), 833-839. | MR 1131493 | Zbl 0779.49046

[BMS] Boccardo, L.-Marcellini, P.-Sbordone, C., L∞-regularity for variational problems with sharp non standard growth conditions, Boll. U.M.I. (7) 4-A (1990), 219-225. | MR 1066774 | Zbl 0711.49058

[Ch] Choe, H. J., Interior behavior of minimizers for certain functionals with non standard growth conditions, Nonlinear Analysis TMA, 19 (1992), 933-945. | MR 1192273 | Zbl 0786.35040

[CF] Cianchi A., A.-Fusco, N., Gradient regularity for minimizers under general growth conditions, J. reine angew. Math., 507 (1999), 15-36. | MR 1670258 | Zbl 0913.49024

[DM] Dall'Aglio, A.-Mascolo, E., Regularity for a class of non linear elliptic systems with non standard growth conditions, To appear.

[ELM1] Esposito, L.-Leonetti, F.-Mingione, G., Regularity for minimizers of functionals with p-q growth, NoDEA Nonlinear Differential Equations Appl., 6 (1999), 133-148. | MR 1694803 | Zbl 0928.35044

[ELM2] Esposito, L.-Leonetti, F.-Mingione, G., Higher integrability for minimizers of integral functionals with p,q growth, J. Differential Equations, 157 (1999), 414-438. | MR 1713266 | Zbl 0939.49021

[FS] Fusco, N.-Sbordone, C., Higher integrability of the gradient of minimizers of functionals with nonstandard growth conditions, Comm. on Pure and Appl. Math., 43 (1990), 673-683. | MR 1057235 | Zbl 0727.49021

[G1] Giaquinta, M., Multiple integrals in the calculus of variations and non linear elliptic systems, Annals of Math. Studies, 105 (1983), Princeton Univ. Press. | MR 717034 | Zbl 0516.49003

[G2] Giaquinta, M., Growth conditions and regularity, a counterexample, Manuscripta Math., 59 (1987), 245-248. | MR 905200 | Zbl 0638.49005

[Gi] Giusti, E., Metodi diretti nel calcolo delle variazioni, U.M.I. (1994). | MR 1707291

[H] Hong, M. C., Some remarks on the minimizers of variational integrals with non standard growth conditions, Boll. U.M.I., 6-A (1992), 91-101. | MR 1164739 | Zbl 0768.49022

[Li] Lieberman, G., The natural generalization of the natural growth conditions of Ladyzhenskaya and Ural'tseva for elliptic equations, Comm. Partial Differential Equations, 16 (1991), 311-361. | MR 1104103 | Zbl 0742.35028

[M1] Marcellini, P., Un example de solution discontinue d'un probléme variationel dans le cas scalaire, Preprint Ist. «U. Dini», Firenze (1987).

[M2] Marcellini, P., Regularity of minimizers of integrals in the calculus of variations with non standard growth conditions, Arch. Rat. Mech. and Analysis, 105 (1989), 267-284. | MR 969900 | Zbl 0667.49032

[M3] Marcellini, P., Regularity and existence of solutions of elliptic equations with p, q-growth conditions, J. Diff. Equat., 90 (1991), 1-30. | MR 1094446 | Zbl 0724.35043

[M4] Marcellini, P., Everywhere regularity for a class of elliptic systems without growth conditions, Ann. Scuola Norm. Sup. Pisa, Cl. sci., 23 (1996), 1-25. | MR 1401415 | Zbl 0922.35031