| Full text | |
| Author(s): |
Total Authors: 3
|
| Affiliation: | [1] Univ Estadual Campinas, Dept Matemat, IMECC, BR-13083859 Campinas, SP - Brazil
[2] Univ Fed Ceara, Dept Matemat, BR-60455760 Fortaleza, Ceara - Brazil
Total Affiliations: 2
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| Document type: | Journal article |
| Source: | MATHEMATISCHE ANNALEN; v. 351, n. 1, p. 215-250, SEP 2011. |
| Web of Science Citations: | 1 |
| Abstract | |
We establish existence and sharp regularity results for solutions to singular elliptic equations of the order u(-beta), 0 < beta < 1, with gradient dependence and involving a forcing term lambda f (x, u). Our approach is based on a singularly perturbed technique. We show that if the forcing parameter lambda > 0 is large enough, our solution is positive. For lambda small solutions vanish on a nontrivial set and therefore they exhibit free boundaries. We also establish regularity results for the free boundary and study the asymptotic behavior of the problem as beta SE arrow 0 and beta NE arrow 1. In the former, we show that our solutions u(beta) converge to a C(1,1) function which is a solution to an obstacle type problem. When beta NE arrow 1 we recover the Alt-Caffarelli theory. (AU) | |
| FAPESP's process: | 08/01458-2 - Partial differential equations and curvature flows |
| Grantee: | Olivâine Santana de Queiroz |
| Support Opportunities: | Scholarships in Brazil - Post-Doctoral |