Weighted Eigenvalue Problems for Fourth-Order Operators in Degenerating Annuli

Autor:	Michelat, Alexis, Rivière, Tristan
Rok vydání:	2023
Předmět:	Mathematics - Analysis of PDEs Mathematics - Differential Geometry 15A18 15A42 34L15 35P15 58J05 58E05 35A15 35J20
Druh dokumentu:	Working Paper
Popis:	We obtain a nigh optimal estimate for the first eigenvalue of two natural weighted problems associated to the bilaplacian (and of a continuous family of fourth-order elliptic operators in dimension $2$) in degenerating annuli (that are central objects in bubble tree analysis) in all dimension. The estimate depends only on the conformal class of the annulus. We also show that in dimension $2$ and dimension $4$, the first eigenfunction (of the first problem) is never radial provided that the conformal class of the annulus is large enough. The other result is a weighted Poincar\'e-type inequality in annuli for those fourth-order operators. Applications to Morse theory are given. Comment: 124 pages, 1 figure
Databáze:	arXiv
Externí odkaz:	http://arxiv.org/abs/2306.04609 Zobrazit plný text záznamu View this record from Arxiv