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arXiv · 2308.04157

Refinement of asymptotic behavior of the eigenvalues for the linearized Liouville-Gel'fand Problem

Hiroshi Ohtsuka·Tomohiko Sato
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Abstract

We determine the second term of the asymptotic expansions for the first m eigenvalues and eigenfunctions of the linearized Liouville-Gel'fand problem associated to solutions which blow-up at m points. Our problem is the case with an inhomogeneous coefficient in two dimensional domain and we extend the previous studies for the problem with a homogeneous coefficient. We also discuss in detail the required regularity of the coefficient necessary to get the conclusion.

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Hiroshi Ohtsuka, Tomohiko Sato. 2023-08-08. Refinement of asymptotic behavior of the eigenvalues for the linearized Liouville-Gel'fand Problem. https://arxiv.org/abs/2308.04157

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