Some weighted Poincare inequalities Fausto FerrariEnrico Valdinoci 35J6035J20weighted Poincare inequalitiessemilinear equations Using stable solutions of suitable PDEs, we obtain some weighted Poincar\'e inequalities, with applications to the Laplace operator in the Euclidean space, to the real part of the Laplace-Kohn operator in the Heisenberg group, to the sub-laplacian in the Engel group, to the Franchi-Grushin-Lanconelli operators,and the $p$-laplacian in the Euclidean space. Indiana University Mathematics Journal 2009 text pdf 10.1512/iumj.2009.58.3601 10.1512/iumj.2009.58.3601 en Indiana Univ. Math. J. 58 (2009) 1619 - 1638 state-of-the-art mathematics http://iumj.org/access/