| Full text | |
| Author(s): |
Bonheure, Denis
[1]
;
Foldes, Juraj
[2]
;
Dos Santos, Ederson Moreira
[3]
;
Saldana, Alberto
[4]
;
Tavares, Hugo
[4, 5]
Total Authors: 5
|
| Affiliation: | [1] Univ Libre Bruxelles, Dept Math, CP 214, Blvd Triomphe, B-1050 Brussels - Belgium
[2] Univ Virginia, Dept Math, 141 Cabell Dr, Kerchof Hall, Charlottesville, VA 22904 - USA
[3] Univ Sao Paulo, Inst Ciencias Matemat & Comp, Caixa Postal 668, BR-13560970 Sao Carlos, SP - Brazil
[4] Univ Lisbon, Inst Super Tecn, Dept Matemat, CAMGSD, Av Rovisco Pais, P-1049001 Lisbon - Portugal
[5] Univ Lisbon, Fac Ciencias, Dept Matemat, Edificio C6, Piso 1, P-1749016 Lisbon - Portugal
Total Affiliations: 5
|
| Document type: | Journal article |
| Source: | TRANSACTIONS OF THE AMERICAN MATHEMATICAL SOCIETY; v. 370, n. 10, p. 7081-7127, OCT 2018. |
| Web of Science Citations: | 0 |
| Abstract | |
We prove a general criterion for the uniqueness of critical points of a functional in the presence of constraints such as positivity, boundedness, or fixed mass. Our method relies on convexity properties along suitable paths and significantly generalizes well-known uniqueness theorems. Due to the flexibility in the construction of the paths, our approach does not depend on the convexity of the domain and can be used to prove the uniqueness in subsets, even if it does not hold globally. The results apply to all critical points and not only to minimizers, providing the uniqueness of solutions to the corresponding Euler-Lagrange equations. For functionals emerging from elliptic problems, the assumptions of our abstract theorems follow from maximum principles, decay properties, and novel general inequalities. To illustrate our method we present a unified proof of known results, as well as new theorems for mean-curvature type operators, fractional Laplacians, Hamiltonian systems, Schrodinger equations, and Gross-Pitaevskii systems. (AU) | |
| FAPESP's process: | 14/03805-2 - Nonlinear elliptic partial differential equations and systems |
| Grantee: | Ederson Moreira dos Santos |
| Support Opportunities: | Scholarships abroad - Research |
| FAPESP's process: | 15/17096-6 - Problems on Elliptic PDEs: systems and equations |
| Grantee: | Ederson Moreira dos Santos |
| Support Opportunities: | Regular Research Grants |