Some isoperimetric inequalities with respect to monomial weights

被引：6

作者：

Alvino, Angelo ^{[1
]}

Brock, Friedemann ^{[2
]}

Chiacchio, Francesco ^{[1
]}

Mercaldo, Anna ^{[1
]}

Posteraro, Maria Rosaria ^{[1
]}

机构：

[1] Univ Napoli Federico II, Dipartimento Matemat & Applicaz R Caccioppoli, Complesso Monte S Angelo,Via Cintia, I-80126 Naples, Italy

[2] Univ Rostock, Inst Math, Ulmenstr 69, D-18057 Rostock, Germany

来源：

ESAIM-CONTROL OPTIMISATION AND CALCULUS OF VARIATIONS | 2021年 / 27卷

关键词：

Isoperimetric inequality; weighted Cheeger set; eigenvalue problems; SETS;

D O I：

10.1051/cocv/2020054

中图分类号：

TP [自动化技术、计算机技术];

学科分类号：

0812 ;

摘要：

We solve a class of isoperimetric problems on R-+(2) with respect to monomial weights. Let alpha and beta be real numbers such that 0 <= alpha < beta + 1, beta <= 2 alpha. We show that, among all smooth sets Omega in R-+(2) with fixed weighted measure integral integral (Omega) y(beta) dxdy, the weighted perimeter integral (partial derivative Omega) y(alpha) ds achieves its minimum for a smooth set which is symmetric w.r.t. to the y-axis, and is explicitly given. Our results also imply an estimate of a weighted Cheeger constant and a bound for eigenvalues of some nonlinear problems.

引用

页数：29

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