| Title:
|
On the continuity of minimizers for quasilinear functionals (English) |
| Author:
|
Cruz-Uribe, David |
| Author:
|
Di Gironimo, Patrizia |
| Author:
|
D'Onofrio, Luigi |
| Language:
|
English |
| Journal:
|
Czechoslovak Mathematical Journal |
| ISSN:
|
0011-4642 (print) |
| ISSN:
|
1572-9141 (online) |
| Volume:
|
62 |
| Issue:
|
1 |
| Year:
|
2012 |
| Pages:
|
111-116 |
| Summary lang:
|
English |
| . |
| Category:
|
math |
| . |
| Summary:
|
In this paper we establish a continuity result for local minimizers of some quasilinear functionals that satisfy degenerate elliptic bounds. The non-negative function which measures the degree of degeneracy is assumed to be exponentially integrable. The minimizers are shown to have a modulus of continuity controlled by $\log \log (1/|x|)^{-1}$. Our proof adapts ideas developed for solutions of degenerate elliptic equations by J. Onninen, X. Zhong: Continuity of solutions of linear, degenerate elliptic equations, Ann. Sc. Norm. Super. Pisa Cl. Sci. (5) 6 (2007), 103–116. (English) |
| Keyword:
|
regularity |
| Keyword:
|
quasilinear functionals |
| Keyword:
|
calculus of variations |
| MSC:
|
49J10 |
| MSC:
|
49N60 |
| idZBL:
|
Zbl 1249.49052 |
| idMR:
|
MR2899738 |
| DOI:
|
10.1007/s10587-012-0020-y |
| . |
| Date available:
|
2012-03-05T07:15:39Z |
| Last updated:
|
2020-07-03 |
| Stable URL:
|
http://hdl.handle.net/10338.dmlcz/142044 |
| . |
| Reference:
|
[1] Fusco, N., Hutchinson, J. E.: Partial regularity and everywhere continuity for a model problem from nonlinear elasticity.J. Aust. Math. Soc., Ser. A 57 (1994), 158-169. Zbl 0864.35032, MR 1288671, 10.1017/S1446788700037496 |
| Reference:
|
[2] Gilbarg, D., Trudinger, N. S.: Elliptic Partial Differential Equations of Second Order. Reprint of the 1998 ed.Classics in Mathematics. Springer, Berlin (2001). Zbl 1042.35002, MR 1814364 |
| Reference:
|
[3] Manfredi, J. J.: Weakly monotone functions.J. Geom. Anal. 4 (1994), 393-402. Zbl 0805.35013, MR 1294334, 10.1007/BF02921588 |
| Reference:
|
[4] Morrey, C. B.: On the solutions of quasi-linear elliptic partial differential equations.Trans. Am. Math. Soc. 43 (1938), 126-166. Zbl 0018.40501, MR 1501936, 10.1090/S0002-9947-1938-1501936-8 |
| Reference:
|
[5] Morrey, C. B.: Multiple integral problems in the calculus of variations and related topics.Univ. California Publ. Math., n. Ser. 1 (1943), 1-130. Zbl 0063.04107, MR 0011537 |
| Reference:
|
[6] Onninen, J., Zhong, X.: Continuity of solutions of linear, degenerate elliptic equations.Ann. Sc. Norm. Super. Pisa, Cl. Sci. (5) 6 (2007), 103-116. Zbl 1150.35055, MR 2341517 |
| . |
