| Full text | |
| Author(s): |
Total Authors: 3
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| Affiliation: | [1] Univ Coimbra, Dept Math, CMUC, P-3001501 Coimbra - Portugal
[2] Univ Estadual Campinas, Dept Matemat, IMECC, BR-13083859 Campinas, SP - Brazil
[3] Univ Fed Ceara, BR-60455760 Fortaleza, Ceara - Brazil
Total Affiliations: 3
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| Document type: | Journal article |
| Source: | ANNALES DE L' INSTITUT HENRI POINCARÉ-ANALYSE NON LINÉAIRE; v. 32, n. 4, p. 741-762, JUL-AUG 2015. |
| Web of Science Citations: | 9 |
| Abstract | |
We provide a rather complete description of the sharp regularity theory to a family of heterogeneous, two-phase free boundary problems, J(gamma) -> min, ruled by nonlinear, p-degenerate elliptic operators. Included in such family are heterogeneous cavitation problems of Prandtl-Batchelor type, singular degenerate elliptic equations; and obstacle type systems. The Euler-Lagrange equation associated to J(gamma) becomes singular along the free interface [u = 0]. The degree of singularity is, in turn, dimmed by the parameter gamma epsilon {[}0, 1]. For 0 < gamma < 1 we show that local minima are locally of class C-1,C-alpha for alpha sharp a that depends on dimension, p and gamma. For gamma = 0 we obtain a quantitative, asymptotically optimal result, which assures that local minima are Log-Lipschitz continuous. The results proven in this article are new even in the classical context of linear, nondegenerate equations. (C) 2014 Elsevier Masson SAS. All rights reserved. (AU) | |
| FAPESP's process: | 12/20197-0 - Local aspects of eliptic and parabolic problems |
| Grantee: | Olivâine Santana de Queiroz |
| Support Opportunities: | Regular Research Grants |