Weighted Sobolev's inequalities for bounded domains and singular elliptic equations Duong DucNguyen Cong PhucNguyen Truyen 26D1046E3542B20weighted Sobolev's inequalitiesfractional integralsGreen functionsH\"older regularitysingular elliptic functions 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. Indiana University Mathematics Journal 2007 text pdf 10.1512/iumj.2007.56.2840 10.1512/iumj.2007.56.2840 en Indiana Univ. Math. J. 56 (2007) 615 - 642 state-of-the-art mathematics http://iumj.org/access/