A new weight class and Poincaré inequalities with the Radon measure. (English) Zbl 1279.26038

Summary: We first introduce and study a new family of weights, the \(A(\alpha, \beta, \gamma, E)\)-class which contains the well-known \(A_r(E)\)-weight as a proper subset. Then, as applications of the \(A(\alpha,\beta, \gamma;E)\)-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.


26D10 Inequalities involving derivatives and differential and integral operators
35J60 Nonlinear elliptic equations
31B05 Harmonic, subharmonic, superharmonic functions in higher dimensions
58A10 Differential forms in global analysis
46E35 Sobolev spaces and other spaces of “smooth” functions, embedding theorems, trace theorems
Full Text: DOI


[1] doi:10.1016/j.jmaa.2007.05.078 · Zbl 1138.47037 · doi:10.1016/j.jmaa.2007.05.078
[2] doi:10.1006/jmaa.2000.6851 · Zbl 0959.58002 · doi:10.1006/jmaa.2000.6851
[3] doi:10.1016/S0022-247X(02)00331-1 · Zbl 1035.46024 · doi:10.1016/S0022-247X(02)00331-1
[4] doi:10.1155/S0161171202107046 · Zbl 1014.30014 · doi:10.1155/S0161171202107046
[5] doi:10.1016/j.camwa.2004.06.006 · Zbl 1155.31303 · doi:10.1016/j.camwa.2004.06.006
[6] doi:10.1016/S0022-247X(03)00036-2 · Zbl 1021.31004 · doi:10.1016/S0022-247X(03)00036-2
[7] doi:10.1006/jmaa.1998.6096 · Zbl 0918.26013 · doi:10.1006/jmaa.1998.6096
[8] doi:10.1016/S0022-247X(03)00216-6 · Zbl 1027.30053 · doi:10.1016/S0022-247X(03)00216-6
[9] doi:10.1007/BF00411477 · Zbl 0793.58002 · doi:10.1007/BF00411477
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.