scholarly journals Regularity of solutions to fully nonlinear elliptic and parabolic free boundary problems

2016 ◽  
Vol 33 (5) ◽  
pp. 1259-1277 ◽  
Author(s):  
Emanuel Indrei ◽  
Andreas Minne
Keyword(s):  
Free Boundary ◽  
Free Boundary Problems ◽  
Regularity Of Solutions ◽  
Boundary Problems ◽  
Fully Nonlinear ◽  
Nonlinear Elliptic

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 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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