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Stable solutions of the Allen-Cahn equation in dimension 8 and minimal cones.

Abstract : For all n \geq 1, we are interested in bounded solutions of the Allen-Cahn equation \Delta u+ u− u^3 = 0 which are defined in all R^{n+1} and whose zero set is asymptotic to a given minimal cone. In particular, in dimension n + 1 \geq 8, we prove the existence of stable solutions of the Allen-Cahn equation whose zero sets are not hyperplanes.
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https://hal.archives-ouvertes.fr/hal-00851587
Contributor : Carole Juppin <>
Submitted on : Thursday, August 15, 2013 - 12:20:54 AM
Last modification on : Thursday, March 5, 2020 - 6:26:00 PM

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  • HAL Id : hal-00851587, version 1

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Frank Pacard, Juncheng Wei. Stable solutions of the Allen-Cahn equation in dimension 8 and minimal cones.. Journal of Functional Analysis, Elsevier, 2013, 264 (5), pp.1131-1167. ⟨hal-00851587⟩

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