具有受控莫尔斯指数的帕莱-斯马尔序列的紧凑性，适用于刘维尔型函数

arXiv - MATH - Analysis of PDEs Pub Date : 2024-09-10 DOI:arxiv-2409.06515

Francesco Malizia

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引用次数: 0

摘要

我们证明，只要闭合曲面上的Liouville型函数的Palais-Smale序列满足其莫尔斯指数的约束，它们就是前紧凑的。作为副产品，我们得到了一个新的证明，即在超临界状态下，Liouville 型均场方程的解的存在性。此外，我们还讨论了将这一结果推广到奇异Liouville方程的情况。

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

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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arXiv - MATH - Analysis of PDEs

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