Differential and Integral Equations

Radó type removability result for fully nonlinear equations

Kazuhiro Takimoto

Full-text: Access denied (no subscription detected) We're sorry, but we are unable to provide you with the full text of this article because we are not able to identify you as a subscriber. If you have a personal subscription to this journal, then please login. If you are already logged in, then you may need to update your profile to register your subscription. Read more about accessing full-text

Abstract

We consider the removability of a level set for solutions to fully nonlinear elliptic and parabolic equations. We prove that if a $C^1$ function $u$ is a viscosity solution to the fully nonlinear equation $F(x,u,Du,D^2u)=0$ or $u_t + F(t,x,u,Du,D^2u)=0$ in a domain outside the zero-level set of $u$, then $u$ is indeed a viscosity solution to the same equation in the whole domain, under some hypotheses on $F$. We also establish the removability result for singular fully nonlinear equations.

Article information

Source
Differential Integral Equations Volume 20, Number 8 (2007), 939-960.

Dates
First available in Project Euclid: 20 December 2012

Permanent link to this document
https://projecteuclid.org/euclid.die/1356039365

Mathematical Reviews number (MathSciNet)
MR2339844

Zentralblatt MATH identifier
1212.35034

Subjects
Primary: 35B60
Secondary: 35D05 35J70 35K70: Ultraparabolic equations, pseudoparabolic equations, etc.

Citation

Takimoto, Kazuhiro. Radó type removability result for fully nonlinear equations. Differential Integral Equations 20 (2007), no. 8, 939--960. https://projecteuclid.org/euclid.die/1356039365.


Export citation