| Title:
|
Some remarks on the regularity of minimizers of integrals with anisotropic growth (English) |
| Author:
|
Bhattacharya, Tilak |
| Author:
|
Leonetti, Francesco |
| Language:
|
English |
| Journal:
|
Commentationes Mathematicae Universitatis Carolinae |
| ISSN:
|
0010-2628 (print) |
| ISSN:
|
1213-7243 (online) |
| Volume:
|
34 |
| Issue:
|
4 |
| Year:
|
1993 |
| Pages:
|
597-611 |
| . |
| Category:
|
math |
| . |
| 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. (English) |
| Keyword:
|
regularity |
| Keyword:
|
minimizers |
| Keyword:
|
integral functionals |
| Keyword:
|
anisotropic growth |
| MSC:
|
35J35 |
| MSC:
|
35J60 |
| MSC:
|
49N60 |
| idZBL:
|
Zbl 0794.49034 |
| idMR:
|
MR1263791 |
| . |
| Date available:
|
2009-01-08T18:06:47Z |
| Last updated:
|
2012-04-30 |
| Stable URL:
|
http://hdl.handle.net/10338.dmlcz/118619 |
| . |
| Reference:
|
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| Reference:
|
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| Reference:
|
[3] Adams R.A.: Sobolev Spaces.New York, 1975. Zbl 1098.46001, MR 0450957 |
| Reference:
|
[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 |
| Reference:
|
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| Reference:
|
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| Reference:
|
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| Reference:
|
[8] Fusco N., Sbordone C.: Local boundedness of minimizers in a limit case.Manuscripta Math. 69 (1990), 19-25. Zbl 0722.49012, MR 1070292 |
| Reference:
|
[9] Fusco N., Sbordone C.: Some remarks on the regularity of minima of anisotropic integrals.Comm. P.D.E. 18 (1993), 153-167. Zbl 0795.49025, MR 1211728 |
| Reference:
|
[10] Giaquinta M.: Growth conditions and regularity, a counterexample.Manuscripta Math. 59 (1987), 245-248. Zbl 0638.49005, MR 0905200 |
| Reference:
|
[11] Giaquinta M.: Multiple integrals in the calculus of variations and nonlinear elliptic systems.Princeton, 1983. Zbl 0516.49003, MR 0717034 |
| Reference:
|
[12] Leonetti F.: Weak differentiability for solutions to nonlinear elliptic systems with p,q-growth conditions.Ann. Mat. Pura Appl. 162 (1992), 349-366. Zbl 0801.35023, MR 1199662 |
| Reference:
|
[13] Leonetti F.: Higher integrability for minimizers of integral functionals with nonstandard growth.J. Differential Equations, to appear. Zbl 0813.49030, MR 1293473 |
| Reference:
|
[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 |
| Reference:
|
[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. |
| Reference:
|
[16] Troisi M.: Teoremi di inclusione per spazi di Sobolev non isotropi.Ricerche di Mat. 18 (1969), 3-24. Zbl 0182.16802, MR 0415302 |
| . |
