Multiplicity results for mass constrained Allen–Cahn equations on Riemannian manifolds with boundary
Year: 2025
Type: article
Abstract: We present multiplicity results for mass constrained Allen–Cahn equations on a Riemannian manifold with boundary, considering both Neumann and Dirichlet conditions. These results hold under the assumptions of small mass constraint and small diffusion parameter. We obtain lower bounds on the number of solutions according to the Lusternik–Schnirelmann category of the manifold in case of Dirichlet boundary conditions and of its boundary in the case of Neumann boundary conditions. Under generic non-degeneracy assumptions on the solutions, we obtain stronger results based on Morse inequalities. Our approach combines topological and variational methods with tools from Geometric Measure Theory.
Source: Mathematische Annalen
Language: English
Subfield: Applied Mathematics
Field: Mathematics
Domain: Physical Sciences
Open Access status: hybrid
Estimated APC paid: $3,190
Awards: G321761023, Modern methods in differential geometry and geometric analysis, Orthogonal geodesics in manifolds with singular boundary. Applications to the theory of minimal surfaces., Breaking new ground in the ACH equation: a research partnership between São Paulo and UNICAM, G6438247056, Geometric variational problems: existence, regularity and geometrical characterization of the solutions
OpenAlex ID: W4410141129