| Full text | |
| Author(s): |
Benci, Vieri
;
Nardulli, Stefano
;
Piccione, Paolo
;
Acevedo, Luis Eduardo Osorio
Total Authors: 4
|
| Document type: | Journal article |
| Source: | NONLINEAR ANALYSIS-THEORY METHODS & APPLICATIONS; v. 220, p. 29-pg., 2022-03-18. |
| Abstract | |
We give a multiplicity result for solutions of the Van der Waals-Cahn-Hilliard two phase transition equation with volume constraints on a closed Riemannian manifold. Our proof employs some results from the classical Lusternik-Schnirelman and Morse theory, together with a technique, the so-called photography method, which allows us to obtain lower bounds on the number of solutions in terms of topological invariants of the underlying manifold. The setup for the photography method employs recent results from Riemannian isoperimetry for small volumes. (C)& nbsp;2022 Elsevier Ltd. All rights reserved. (AU) | |
| FAPESP's process: | 16/23746-6 - Algebraic, topological and analytical techniques in differential geometry and geometric analysis |
| Grantee: | Paolo Piccione |
| Support Opportunities: | Research Projects - Thematic Grants |
| FAPESP's process: | 21/05256-0 - Geometric variational problems: existence, regularity and geometrical characterization of the solutions |
| Grantee: | Stefano Nardulli |
| Support Opportunities: | Research Grants - Young Investigators Grants |
| FAPESP's process: | 17/13155-3 - Geometric measure Theory and Isoperimetric problems |
| Grantee: | Luis Eduardo Osorio Acevedo |
| Support Opportunities: | Scholarships in Brazil - Post-Doctoral |
| FAPESP's process: | 18/22938-4 - Boundary regularity for area minimizing currents |
| Grantee: | Stefano Nardulli |
| Support Opportunities: | Scholarships abroad - Research |