Published Paper
Inserted: 14 jul 2020
Last Updated: 30 mar 2022
Journal: Nonlinear Analysis
Pages: 30
Year: 2022
Doi: 10.1016/j.na.2022.112851
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Published version
Abstract:
WegiveamultiplicityresultforsolutionsoftheVanderWaals-Cahn-Hilliard two-phase transition equation with volume constraints on a closed Riemannian manifold. Our proof employs some results from the classical LusternikāSchnirelman and Morse theory, together with a technique, the so-called 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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