We consider a class of isoperimetric problems on $R^{N}_{+}$ where the volume and the area element carry two different weights of the type $|x|^{l}x_{N}^{alpha}$. We solve them in a special case while a more detailed study is contained in [2]. Our results imply a weighted Polya-Szego principle and a priori estimates for weak solutions to a class of boundary value problems for degenerate elliptic equations.
On weighted isoperimetrc inequalities with non radial densities / Alvino, Angelo; Brock, Friedemann; Chiacchio, Francesco; Mercaldo, Anna; Posteraro, MARIA ROSARIA. - In: APPLICABLE ANALYSIS. - ISSN 0003-6811. - 98:10(2019), pp. 1935-1945. [10.1080/00036811.2018.1506106]
On weighted isoperimetrc inequalities with non radial densities
Angelo Alvino;Francesco Chiacchio
;Anna Mercaldo;Maria Rosaria Posteraro
2019
Abstract
We consider a class of isoperimetric problems on $R^{N}_{+}$ where the volume and the area element carry two different weights of the type $|x|^{l}x_{N}^{alpha}$. We solve them in a special case while a more detailed study is contained in [2]. Our results imply a weighted Polya-Szego principle and a priori estimates for weak solutions to a class of boundary value problems for degenerate elliptic equations.I documenti in IRIS sono protetti da copyright e tutti i diritti sono riservati, salvo diversa indicazione.