log-concavity of eigenfunction and Brunn-Minkowski inequality of eigenvalue for weighted p-Laplace operator

Lei Qin

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arXiv · 2411.16377

log-concavity of eigenfunction and Brunn-Minkowski inequality of eigenvalue for weighted p-Laplace operator

Lei Qin

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Abstract

In this paper, we investigate the log-concavity property of the first eigenfunction to the weighted $p$-Laplace operator in class of bounded, convex and smooth domain. Moreover, we prove a Brunn-Minkowski-type inequality for the first eigenvalue to the weighted $p$-Laplace operator in the class of $C^2$ convex bodies in $\R^n$

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Lei Qin. 2024-11-25. log-concavity of eigenfunction and Brunn-Minkowski inequality of eigenvalue for weighted p-Laplace operator. https://arxiv.org/abs/2411.16377

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