Multiple solutions for the Van der Waals--Allen--Cahn--Hilliard equation with a volume constraint

created by nardulli on 31 Jul 2019

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Submitted Paper

Inserted: 31 jul 2019
Last Updated: 31 jul 2019

Year: 2019

ArXiv: 1907.12689 PDF

Abstract:

We give multiplicity results for the solutions of a nonlinear elliptic equation, with an asymmetric double well potential of Van der Waals-Allen--Cahn--Hilliard type, satisfying a linear volume constraint, on a bounded Lipschitz domain $\Omega\subset\mathds R^N$. The number of solutions is estimated in terms of topological and homological invariants of the underlying domain $\Omega$.

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