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arXiv · 2409.06515

Compactness of Palais-Smale sequences with controlled Morse Index for a Liouville type functional

Francesco Malizia
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Abstract

We prove that Palais-Smale sequences for Liouville type functionals on closed surfaces are precompact whenever they satisfy a bound on their Morse index. As a byproduct, we obtain a new proof of existence of solutions for Liouville type mean-field equations in a supercritical regime. Moreover, we also discuss an extension of this result to the case of singular Liouville equations.

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Francesco Malizia. 2024-09-10. Compactness of Palais-Smale sequences with controlled Morse Index for a Liouville type functional. https://arxiv.org/abs/2409.06515

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