Desigualdades isoperimétricas com pesos monomiais

Abstract

We consider the monomial weight |x_1|^{A_1}...|x_n|^{A_n} in R^n, where A_i ≥ 0 is a real number for each i = 1, ..., n, and we present the isoperimetric, Sobolev, Morrey, and Trudinger-Moser inequalities involving this weight. They are the analogue of the classical ones with the Lebesgue measure dx replaced by |x_1|^{A_1}...|x_n|^{A_n}dx. For the isoperimetric and Sobolev inequalities, we describe the best constant and the extremal functions.