## Differential and Integral Equations

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

### Radó type removability result for fully nonlinear equations

#### 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