| Autor: |
Catino, Giovanni, Li, Yanyan, Monticelli, Dario D., Roncoroni, Alberto |
| Rok vydání: |
2023 |
| Předmět: |
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| Druh dokumentu: |
Working Paper |
| Popis: |
In this paper we classify positive solutions to the critical semilinear elliptic equation in $\mathbb{H}^n$. We prove that they are the Jerison-Lee's bubbles, provided $n=1$ or $n\geq 2$ and a suitable control at infinity holds. The proofs are based on a classical Jerison-Lee's differential identity and on pointwise/integral estimates recently obtained for critical semilinear and quasilinear elliptic equations in $\mathbb{R}^n$. In particular, the result in $\mathbb{H}^1$ can be seen as the analogue of the celebrated Caffarelli-Gidas-Spruck classification theorem. |
| Databáze: |
arXiv |
| Externí odkaz: |
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