Differential and Integral Equations

Král type removability results for $k$-Hessian equation and $k$-curvature equation

Kazuhiro Takimoto

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Abstract

We consider some removability problem for solutions to the so-called $k$-Hessian equation and $k$-curvature equation. We prove that if a $C^1$ function $u$ is a generalized solution to $k$-Hessian equation $F_k[u]=g(x,u,Du)$ or $k$-curvature equation $H_k[u]=g(x,u,Du)$ in $\Omega \setminus u^{-1}(E)$ for $E \subset \mathbb{R}$, then it is indeed a generalized solution to the same equation in the whole domain $\Omega$, under some hypotheses on $u$, $g$ and $E$.

Article information

Source
Differential Integral Equations, Volume 32, Number 3/4 (2019), 211-222.

Dates
First available in Project Euclid: 23 January 2019

Permanent link to this document
https://projecteuclid.org/euclid.die/1548212429

Mathematical Reviews number (MathSciNet)
MR3909984

Zentralblatt MATH identifier
07036980

Subjects
Primary: 35B60: Continuation and prolongation of solutions [See also 58A15, 58A17, 58Hxx] 35D99: None of the above, but in this section 35J60: Nonlinear elliptic equations 35J70: Degenerate elliptic equations

Citation

Takimoto, Kazuhiro. Král type removability results for $k$-Hessian equation and $k$-curvature equation. Differential Integral Equations 32 (2019), no. 3/4, 211--222. https://projecteuclid.org/euclid.die/1548212429


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