Year: 2026
Type: preprint
Abstract: In this paper we prove a quantization property for Palais-Smale sequences of functionals related to Liouville equations on compact surfaces. While these equations have been extensively studied over the past decades, such a quantization property had not been established so far, and has been often bypassed by the Struwe monotonicity trick. Our result, which relies on careful $L^p$ estimates to obtain gradient bounds and to perform neck analysis, allows to directly apply variational methods to obtain existence of solutions in non-resonant regimes. We also give an example of clustering of blow-up points and a stronger assumption that, on the contrary, guarantees that the blow-up points are isolated.
Source: arXiv (Cornell University)
Institutions: Scuola Normale Superiore, Sapienza University of Rome
Language: English
Subfield: Applied Mathematics
Field: Mathematics
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W7213942220