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01 February 2007 An unstable elliptic free boundary problem arising in solid combustion
R. Monneau, G. S. Weiss
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Duke Math. J. 136(2): 321-341 (01 February 2007). DOI: 10.1215/S0012-7094-07-13624-X

Abstract

We prove a regularity result for the unstable elliptic free boundary problem Δu=-χ{u>0} related to traveling waves in a problem arising in solid combustion. The maximal solution and every local minimizer of the energy are regular; that is, {u=0} is locally an analytic surface, and u|{u>0}̲,u|{u<0}̲ are locally analytic functions. Moreover, we prove a partial regularity result for solutions that are nondegenerate of second order. Here {u=0} is analytic up to a closed set of Hausdorff dimension n-2. We discuss possible singularities

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R. Monneau. G. S. Weiss. "An unstable elliptic free boundary problem arising in solid combustion." Duke Math. J. 136 (2) 321 - 341, 01 February 2007. https://doi.org/10.1215/S0012-7094-07-13624-X

Information

Published: 01 February 2007
First available in Project Euclid: 21 December 2006

zbMATH: 1119.35123
MathSciNet: MR2286633
Digital Object Identifier: 10.1215/S0012-7094-07-13624-X

Subjects:
Primary: 35B65 , 35R35
Secondary: 35J60

Rights: Copyright © 2007 Duke University Press

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Vol.136 • No. 2 • 01 February 2007
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