Multiplicity results for mass constrained Allen–Cahn equations on Riemannian manifolds with boundary
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.
Authors
- Dario Corona (ORCID: https://orcid.org/0000-0002-7575-710X)
- Stefano Nardulli (ORCID: https://orcid.org/0000-0001-9690-1679)
- P. Piccione
- Ramon Oliver-Bonafoux (ORCID: https://orcid.org/0000-0002-6462-0570)
- Giandomenico Orlandi
Institutions
- Università di Camerino (IT)
- University of Verona (IT)
- Zhejiang Normal University (CN)
- Universidade de São Paulo (BR)
- Great Lakes Research Group (United States) (US)
- Universidade Federal do ABC (BR)
Publication Details
- Journal
- Mathematische Annalen
- Published
- 2025-05-07
- DOI
- https://doi.org/10.1007/s00208-025-03178-7
- Citations
- 1
- Primary Topic
- Nonlinear Partial Differential Equations
- Type
- article
- Field-Weighted Citation Impact
- 3.73
Funders
- Istituto Nazionale di Alta Matematica "Francesco Severi"
- Fundação de Amparo à Pesquisa do Estado de São Paulo
- Conselho Nacional de Desenvolvimento Científico e Tecnológico
- Università degli Studi di Verona