Blowup analysis for integral equations on bounded domains

Qianqiao Guo

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arXiv · 1808.08723

Blowup analysis for integral equations on bounded domains

Qianqiao Guo

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Abstract

Consider the integral equation \begin{equation*} f^{q-1}(x)=\int_\Omega\frac{f(y)}{|x-y|^{n-\alpha}}dy,\ \ f(x)>0,\quad x\in \overline \Omega, \end{equation*} where $\Omega\subset \mathbb{R}^n$ is a smooth bounded domain. For $1<\alpha n$, the existence of energy minimizing positive solution in subcritical case $0 n$) are analyzed. We see that for $1<\alpha n$, different phenomena appears.

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Qianqiao Guo. 2018-08-27. Blowup analysis for integral equations on bounded domains. https://arxiv.org/abs/1808.08723

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