Title: Weighted Sobolev's inequalities for bounded domains and singular elliptic equations

Authors: Nguyen Van Truyen, Duong Minh Duc and Nguyen Cong Phuc

Issue: Volume 56 (2007), Issue 2, 615-642

Abstract: Using a method developed by P\'erez and Wheeden and the representation of smooth functions by integral operators whose kernels are gradients of the Green functions, we obtain weighted Sobolev's inequalities for bounded domains which improve and unify several kinds of inequalities. From these results we establish Green functions and the existence, uniqueness and regularit results for a class of singular elliptic equations.