Calculus of Variations and Geometric Measure Theory

SOME SOLUTIONS TO THE CAHN-HILLIARD EQUATION AND CONSTANT MEAN CURVATURE SURFACES

Matteo Rizzi

created by malchiodi on 17 Jun 2019

20 jun 2019 -- 12:00   [open in google calendar]

Scuola Normale Superiore, Aula Bianchi

Abstract.

In the talk I will present the construction of a family $u_\epsilon$ of solutions to the Cahn-Hilliard equation whose zero level set is prescribed and approaches, as $\epsilon \to 0$, a given complete, embedded, $k$-ended constant mean curvature surface. It is a joint work with Michal Kowalczyk. Moreover, I will present some classification results, dealing with properties such as boundedness, monotonicity and radial symmetry.