A blow-up approach for a priori bounds in semilinear planar elliptic systems: the Brezis-Merle critical case
Fuente:
arXiv
Enregistré dans:
| Auteurs principaux: | , , |
|---|---|
| Format: | Preprint |
| Publié: |
2026
|
| Sujets: | |
| Accès en ligne: | |
| Tags: |
Ajouter un tag
Pas de tags, Soyez le premier à ajouter un tag!
|
| _version_ | 1866912938297655296 |
|---|---|
| author | Baldelli, Laura Mancini, Gabriele Romani, Giulio |
| author_facet | Baldelli, Laura Mancini, Gabriele Romani, Giulio |
| contents | We establish uniform a priori estimates for solutions of semilinear planar Hamiltonian elliptic systems in a ball with Dirichlet boundary conditions. We consider a broad class of coupled nonlinearities with asymptotic critical behaviour in the sense of Brezis--Merle. The approach we follow is based on a blow-up analysis combined with Liouville--type theorems and integral estimates. Our results extend the scalar theory of uniform a priori bounds to the Hamiltonian case, and solve an open problem in [de Figueiredo D.G., do Ó J.M., Ruf B., Adv. Nonlinear Stud. 6 (2006), no. 2]. We believe that this approach is new in this setting. As a consequence of our a priori estimates, we prove the existence of a positive solution by means of Fixed Point Index theory. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2602_11720 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | A blow-up approach for a priori bounds in semilinear planar elliptic systems: the Brezis-Merle critical case Baldelli, Laura Mancini, Gabriele Romani, Giulio Analysis of PDEs 35B45 35J57 35B33 35B44 We establish uniform a priori estimates for solutions of semilinear planar Hamiltonian elliptic systems in a ball with Dirichlet boundary conditions. We consider a broad class of coupled nonlinearities with asymptotic critical behaviour in the sense of Brezis--Merle. The approach we follow is based on a blow-up analysis combined with Liouville--type theorems and integral estimates. Our results extend the scalar theory of uniform a priori bounds to the Hamiltonian case, and solve an open problem in [de Figueiredo D.G., do Ó J.M., Ruf B., Adv. Nonlinear Stud. 6 (2006), no. 2]. We believe that this approach is new in this setting. As a consequence of our a priori estimates, we prove the existence of a positive solution by means of Fixed Point Index theory. |
| title | A blow-up approach for a priori bounds in semilinear planar elliptic systems: the Brezis-Merle critical case |
| topic | Analysis of PDEs 35B45 35J57 35B33 35B44 |
| url | https://arxiv.org/abs/2602.11720 |