<Reference List> | |
Type: | Preprint |
National /International: | International |
Title: | Regularity of interfaces for a Pucci type segregation problem |
Publication Date: | 2018-03-05 |
Authors: |
- Luis A. Caffarelli
- S. Patrizi - Veronica Quitalo - M. Torres |
Abstract: | We show the existence of a Lipschitz viscosity solution u in Ω to a system of fully nonlinear equations involving Pucci-type operators. We study the regularity of the interface ∂{u > 0}∩Ω and we show that the viscosity inequalities of the system imply, in the weak sense, the free boundary condition u+ν+ = u−ν−, and hence u is a solution to a two-phase free boundary problem. We show that we can apply the classical method of sup-convolutions developed by the first author in [5,6], and generalized by Wang [20,21] and Feldman [11] to fully nonlinear operators, to conclude that the regular points in ∂{u > 0} ∩ Ω form an open set of class C1,α. A novelty in our problem is that we have different operators, F+ and F−, on each side of the free boundary. In the particular case when these operators are the Pucci’s extremal operators M+ and M−, our results provide an alternative approach to obtain the stationary limit of a segregation model of populations with nonlinear diffusion in [19]. |
Institution: | DMUC 18-07 |
Online version: | http://www.mat.uc.pt...prints/eng_2018.html |
Download: | Not available |