A new weight class and Poincaré inequalities with the Radon measure

Correspondence: [email protected]. cn Department of Mathematics, Harbin Institute of Technology, Harbin, China Abstract We first introduce and study a new family of weights, the A(a, b, g; E)-class which contains the well-known Ar(E)-weight as a proper subset. Then, as applications of the A(a, b, g ;E)-class, we prove the local and global Poincaré inequalities with the Radon measure for the solutions of the non-homogeneous A-harmonic equation which belongs to a kind of the nonlinear partial differential equations. 2000 Mathematics Subject Classification: Primary 26D10; Secondary 35J60; 31B05; 58A10; 46E35.