Published Paper

Inserted: 14 jul 2020
Last Updated: 26 feb 2024

Journal: Nonlinear Analysis
Pages: 30
Year: 2022
Doi: 10.1016/j.na.2022.112851

Abstract:

We give a multiplicity result for solutions of the Van der Waals-Cahn-Hilliard two-phase transition equation with volume constraints on a closed Riemannian manifold. Our proof employs some results from the classical Lusternik--Schnirelman and Morse theory, together with a technique, the so-called \emph{photography method}, which allows us to obtain lower bounds on the number of solutions in terms of topological invariants of the underlying manifold. The setup for the photography method employs recent results from Riemannian isoperimetry for small volumes.

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