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2007 Nontrivial compact blow-up sets of lower dimension in a half-space
Mayte Pérez-Llanos, Julio D. Rossi
Differential Integral Equations 20(11): 1211-1228 (2007).

Abstract

In this paper we provide examples of blowing-up solutions to parabolic problems in a half space, ${{\mathbb{R}}}^N_+ \times {{\mathbb{R}}}^M = \{x_N >0 \} \times {{\mathbb{R}}}^M$, with nontrivial blow-up sets of dimension strictly smaller than the space dimension. To this end we prove existence of a nontrivial compactly supported solution to $\nabla (|\nabla \varphi|^{p-2} \nabla \varphi) = \varphi $ in the half space ${{\mathbb{R}}}^N_+ =\{x_N >0\}$ with the nonlinear boundary condition $-|\nabla \varphi|^{p-2} \frac{\partial \varphi}{\partial x_N} = \varphi^{p-1}$ on $\partial {{\mathbb{R}}}^N_+ =\{ x_N =0\}$.

Citation

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Mayte Pérez-Llanos. Julio D. Rossi. "Nontrivial compact blow-up sets of lower dimension in a half-space." Differential Integral Equations 20 (11) 1211 - 1228, 2007.

Information

Published: 2007
First available in Project Euclid: 20 December 2012

zbMATH: 1212.35017
MathSciNet: MR2372423

Subjects:
Primary: 35J65
Secondary: 35B40 , 35J60 , 35K55 , 35K65

Rights: Copyright © 2007 Khayyam Publishing, Inc.

JOURNAL ARTICLE
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Vol.20 • No. 11 • 2007
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