Calculus of Variations and Geometric Measure Theory

V. Benci - S. Nardulli - P. Piccione

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

created by nardulli on 31 Jul 2019
modified on 14 Jul 2020


Published Paper

Inserted: 31 jul 2019
Last Updated: 14 jul 2020

Journal: Calculus of Variations and Partial Differential Equations
Volume: 59
Pages: 31
Year: 2019
Doi: 10.1007/s00526-020-1724-8

ArXiv: 1907.12689 PDF


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 $\Omega$.