Generic nondegeneracy for solutions of the Allen-Cahn equation under a volume constraint in closed manifolds

Abstract

Let $M^n$ be a connected closed smooth manifold, where $n\ge 2$. In this article, we adapt the techniques in Micheletti and Pistoia (2009) and Ghimenti and Micheletti (2011) to prove the generic nondegeneracy for solutions of the Van der Waals-Allen-Cahn-Hilliard equation under a volume constraint in $M$.

8 pages. Minor changes along the text. Correction of Fredholm index in Lemma 4.1

References in corpus (1)

• Lusternik-Schnirelman and Morse theory for the Van der Waals-Cahn-Hilliard equation with volume constraint

Cited by in corpus (2)

• Multiplicity of solutions to the multiphasic Allen-Cahn-Hilliard system with a small volume constraint on closed parallelizable manifolds
• From bubbles to clusters: Multiple solutions to the Allen--Cahn system