Article
Full entry |
PDF
(0.2 MB)
Feedback
PDF
(0.2 MB)
Feedback
Keywords:
regularity; minimizers; integral functionals; anisotropic growth
regularity; minimizers; integral functionals; anisotropic growth
Summary:
We prove higher integrability for minimizers of some integrals of the calculus of variations; such an improved integrability allows us to get existence of weak second derivatives.
References:
[1] Acerbi E., Fusco N.: Partial regularity under anisotropic $(p,q)$ growth conditions. J. Differential Equations, to appear. MR 1260848 | Zbl 0807.49010
[2] Acerbi E., Fusco N.: Regularity for minimizers of non-quadratic functionals: the case $1< p< 2$. J. Math. Anal. Appl. 140 (1989), 115-135. MR 0997847 | Zbl 0686.49004
[3] Adams R.A.: Sobolev Spaces. New York, 1975. MR 0450957 | Zbl 1098.46001
[4] Bhattacharya T., Leonetti F.: $W^{2,2}$ regularity for weak solutions of elliptic systems with nonstandard growth. J. Math. Anal. Appl. 176 (1993), 224-234. MR 1222166
[5] Campanato S.: Sistemi ellittici in forma divergenza. Regolarità all'interno. Pisa, 1980. MR 0668196 | Zbl 0453.35026
[6] Campanato S., Cannarsa P.: Differentiability and partial Hölder continuity of the solutions of nonlinear elliptic systems of order $2m$ with quadratic growth. Ann. Scuola Norm. Sup. Pisa 8 (1981), 285-309. MR 0623938
[7] Campanato S.: Hölder continuity of the solutions of some nonlinear elliptic systems. Adv. in Math. 48 (1983), 16-43. MR 0697613 | Zbl 0519.35027
[8] Fusco N., Sbordone C.: Local boundedness of minimizers in a limit case. Manuscripta Math. 69 (1990), 19-25. MR 1070292 | Zbl 0722.49012
[9] Fusco N., Sbordone C.: Some remarks on the regularity of minima of anisotropic integrals. Comm. P.D.E. 18 (1993), 153-167. MR 1211728 | Zbl 0795.49025
[10] Giaquinta M.: Growth conditions and regularity, a counterexample. Manuscripta Math. 59 (1987), 245-248. MR 0905200 | Zbl 0638.49005
[11] Giaquinta M.: Multiple integrals in the calculus of variations and nonlinear elliptic systems. Princeton, 1983. MR 0717034 | Zbl 0516.49003
[12] Leonetti F.: Weak differentiability for solutions to nonlinear elliptic systems with p,q-growth conditions. Ann. Mat. Pura Appl. 162 (1992), 349-366. MR 1199662 | Zbl 0801.35023
[13] Leonetti F.: Higher integrability for minimizers of integral functionals with nonstandard growth. J. Differential Equations, to appear. MR 1293473 | Zbl 0813.49030
[14] Marcellini P.: Regularity of minimizers of integrals of the calculus of variations with nonstandard growth conditions. Arch. Rational Mech. Anal. 105 (1989), 267-284. MR 0969900
[15] Marcellini P.: Un example de solution discontinue d'un problème variationnel dans ce cas scalaire. preprint Istituto Matematico ``U. Dini'' Universita' di Firenze, 1987/88, n.11.
[16] Troisi M.: Teoremi di inclusione per spazi di Sobolev non isotropi. Ricerche di Mat. 18 (1969), 3-24. MR 0415302 | Zbl 0182.16802
Search
Partner of
