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arXiv · 2303.04464

Blow-up Analysis of Stationary Solutions to a Liouville-Type Equation in 3-D

Francesca Da Lio·Ali Hyder
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Abstract

In this paper we study the asymptotic behavior of sequences of stationary weak solutions to the following Liouville-type equation $-\Delta u=e^u~~~{in }~~~\Omega$, where $\Omega$ is an open set of $R^3$. By improving the partial regularity estimates obtained by the first author for the above equation, we succeed in performing a blow-up analysis without Morrey-type assumptions on the solutions $u$ and on the nonlinearity $e^u.$

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Francesca Da Lio, Ali Hyder. 2023-03-08. Blow-up Analysis of Stationary Solutions to a Liouville-Type Equation in 3-D. https://arxiv.org/abs/2303.04464

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