Periodic solutions to a cahn hilliard willmore equation in the plane
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2018Metadata
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Malchiodi, Andrea
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Periodic solutions to a cahn hilliard willmore equation in the plane
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Abstract
In this paper we construct entire solutions to the phase field equation of Willmore type in the Euclidean plane, where W(u) is the standard double-well potential . Such solutions have a non-trivial profile that shadows a Willmore planar curve, and converge uniformly to as . These solutions give a counterexample to the counterpart of Gibbons' conjecture for the fourth-order counterpart of the Allen-Cahn equation. We also study the x (2)-derivative of these solutions using the special structure of Willmore's equation.
Patrocinador
Project Geometric Variational Problems from Scuola Normale Superiore
MIUR Bando PRIN
2015KB9WPT001
Deutsche Forschungsgemeinschaft (DFG, German Research Foundation)
MA 6290/2-1
Fondo Basal CMM-Chile
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3170111
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Arch. Rational Mech. Anal. 228 (2018) 821–866
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