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March/April 2019 Král type removability results for $k$-Hessian equation and $k$-curvature equation
Kazuhiro Takimoto
Differential Integral Equations 32(3/4): 211-222 (March/April 2019).

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 $E$.

Citation

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Kazuhiro Takimoto. "Král type removability results for $k$-Hessian equation and $k$-curvature equation." Differential Integral Equations 32 (3/4) 211 - 222, March/April 2019.

Information

Published: March/April 2019
First available in Project Euclid: 23 January 2019

zbMATH: 07036980
MathSciNet: MR3909984

Subjects:
Primary: 35B60 , 35D99 , 35J60 , 35J70

Rights: Copyright © 2019 Khayyam Publishing, Inc.

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Vol.32 • No. 3/4 • March/April 2019
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