One-dimensional symmetry and Liouville type results for the fourth order Allen-Cahn equation in ℝN View Full Text


Ontology type: schema:ScholarlyArticle      Open Access: True


Article Info

DATE

2017-01

AUTHORS

Denis Bonheure, François Hamel

ABSTRACT

In this paper, the authors prove an analogue of Gibbons’ conjecture for the extended fourth order Allen-Cahn equation in ℝN, as well as Liouville type results for some solutions converging to the same value at infinity in a given direction. The authors also prove a priori bounds and further one-dimensional symmetry and rigidity results for semilinear fourth order elliptic equations with more general nonlinearities. More... »

PAGES

149-172

References to SciGraph publications

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  • 2003-08. Heteroclinic connections between nonconsecutive equilibria of a fourth order differential equation in CALCULUS OF VARIATIONS AND PARTIAL DIFFERENTIAL EQUATIONS
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    http://scigraph.springernature.com/pub.10.1007/s11401-016-1065-2

    DOI

    http://dx.doi.org/10.1007/s11401-016-1065-2

    DIMENSIONS

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