Optimal regularity of viscosity solutions of fully nonlinear singular equations and their limiting free boundary problems

2006 ◽  
Vol 30 (13) ◽  
Author(s):  
Eduardo Teixeira
Keyword(s):  
Free Boundary ◽  
Viscosity Solutions ◽  
Free Boundary Problems ◽  
Optimal Regularity ◽  
Boundary Problems ◽  
Fully Nonlinear ◽  
Singular Equations

scholarly journals On optimal regularity of free boundary problems and a conjecture of De Giorgi

2005 ◽  
Vol 58 (8) ◽  
pp. 1051-1076 ◽  
Author(s):  
Herbert Koch ◽  
Giovanni Leoni ◽  
Massimiliano Morini
Keyword(s):  
Free Boundary ◽  
Free Boundary Problems ◽  
Optimal Regularity ◽  
Boundary Problems

scholarly journals Lipschitz Regularity of Solutions to Two-phase Free Boundary Problems

2017 ◽  
Vol 2019 (7) ◽  
pp. 2204-2222 ◽  
Author(s):  
D De Silva ◽  
O Savin
Keyword(s):  
Free Boundary ◽  
Viscosity Solutions ◽  
Lipschitz Continuity ◽  
Free Boundary Problems ◽  
Linear Operators ◽  
Regularity Of Solutions ◽  
Two Phase ◽  
Boundary Problems ◽  
Lipschitz Regularity ◽  
Non Linear

AbstractWe prove Lipschitz continuity of viscosity solutions to a class of two-phase free boundary problems governed by fully non-linear operators.

scholarly journals Free boundary problems for tumor growth: A viscosity solutions approach

2016 ◽  
Vol 138 ◽  
pp. 207-228 ◽  
Author(s):  
Inwon C. Kim ◽  
Benoît Perthame ◽  
Panagiotis E. Souganidis
Keyword(s):  
Free Boundary ◽  
Tumor Growth ◽  
Viscosity Solutions ◽  
Free Boundary Problems ◽  
Boundary Problems

scholarly journals Two-Phase Free Boundary Problems: From Existence to Smoothness

2017 ◽  
Vol 17 (2) ◽  
Author(s):  
Daniela De Silva ◽  
Fausto Ferrari ◽  
Sandro Salsa
Keyword(s):  
Free Boundary ◽  
Viscosity Solutions ◽  
Free Boundary Problems ◽  
Elliptic Operators ◽  
Free Boundaries ◽  
Two Phase ◽  
Boundary Problems ◽  
Open Questions

AbstractWe describe the theory we developed in recent times concerning two-phase free boundary problems governed by elliptic operators with forcing terms. Our results range from existence of viscosity solutions to smoothness of both solutions and free boundaries. We also discuss some open questions, possible object of future investigation.

scholarly journals An overview of unconstrained free boundary problems

2015 ◽  
Vol 373 (2050) ◽  
pp. 20140281 ◽  
Author(s):  
Alessio Figalli ◽  
Henrik Shahgholian
Keyword(s):  
Free Boundary ◽  
Unit Ball ◽  
Free Boundary Problems ◽  
Regularity Of Solutions ◽  
Regular Solutions ◽  
Optimal Regularity ◽  
Open Problems ◽  
Boundary Problems ◽  
Matching Problems ◽  
Open Set

In this paper, we present a survey concerning unconstrained free boundary problems of type where B 1 is the unit ball, Ω is an unknown open set, F 1 and F 2 are elliptic operators (admitting regular solutions), and is a functions space to be specified in each case. Our main objective is to discuss a unifying approach to the optimal regularity of solutions to the above matching problems, and list several open problems in this direction.

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