منابع مشابه
Faber-Krahn type inequalities for trees
The Faber-Krahn theorem states that among all bounded domains with the same volume in Rn (with the standard Euclidean metric), a ball that has lowest first Dirichlet eigenvalue. Recently it has been shown that a similar result holds for (semi)regular trees. In this article we show that such a theorem also hold for other classes of (not necessarily non-regular) trees. However, for these new resu...
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When revisiting the Faber-Krahn inequality for the principal pLaplacian eigenvalue of a bounded open set in Rn with smooth boundary, we simply rename it as the p-Faber-Krahn inequality and interestingly find that this inequality may be improved but also characterized through the Maz’ya’s capacity method, the Euclidean volume and the Sobolev-type inequality. 1. The p-Faber-Krahn Inequality Intro...
متن کاملTHE p-FABER-KRAHN INEQUALITY NOTED
When revisiting the Faber-Krahn inequality for the principal pLaplacian eigenvalue of a bounded open set in Rn with smooth boundary, we simply rename it as the p-Faber-Krahn inequality and interestingly find that this inequality may be improved but also characterized through Maz’ya’s capacity method, the Euclidean volume, the Sobolev type inequality and MoserTrudinger’s inequality. 1. The p-Fab...
متن کاملFaber-krahn Inequalities for the Robin-laplacian: a Free Discontinuity Approach
We introduce a new method to prove the isoperimetric property of the ball for the first eigenvalue of the Robin-Laplacian. Our technique applies to a full range of Faber-Krahn inequalities in a nonlinear setting and for non smooth domains, including the open case of the torsional rigidity. The analysis is based on regularity issues for free discontinuity problems in spaces of functions of bound...
متن کاملA Faber-Krahn-type inequality for regular trees
We show a Faber-Krahn-type inequality for regular trees with boundary.
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ژورنال
عنوان ژورنال: Journal of Mathematical Analysis and Applications
سال: 2020
ISSN: 0022-247X
DOI: 10.1016/j.jmaa.2019.123766