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2018 Heteroclinic solutions of Allen-Cahn type equations with a general elliptic operator
Karol Wroński
Topol. Methods Nonlinear Anal. 52(2): 729-738 (2018). DOI: 10.12775/TMNA.2018.010

Abstract

We consider a generalization of the Allen-Cahn type equation in divergence form $-{\rm div}(\nabla G(\nabla u(x,y)))+F_u(x,y,u(x,y))=0$. This is more general than the usual Laplace operator. We prove the existence and regularity of heteroclinic solutions under standard ellipticity and $m$-growth conditions.

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Karol Wroński. "Heteroclinic solutions of Allen-Cahn type equations with a general elliptic operator." Topol. Methods Nonlinear Anal. 52 (2) 729 - 738, 2018. https://doi.org/10.12775/TMNA.2018.010

Information

Published: 2018
First available in Project Euclid: 25 May 2018

zbMATH: 07051689
MathSciNet: MR3915660
Digital Object Identifier: 10.12775/TMNA.2018.010

Rights: Copyright © 2018 Juliusz P. Schauder Centre for Nonlinear Studies

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Vol.52 • No. 2 • 2018
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