Path:  Home   >  Publication Information
Regularity of interfaces for a Pucci type segregation problem
  <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+ = uν, 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:
Download: Not available
© 2012 Centre for Mathematics, University of Coimbra, funded by

Science and Technology Foundation

Powered by: rdOnWeb v1.4 | technical support