Illinois Journal of Mathematics

Weighted Poincaré inequalities for solutions to $A$-harmonic equations

Shusen Ding and Craig A. Nolder

Full-text: Open access

Abstract

We first prove a local $A_r$-weighted Poincaré inequality for solutions to $A$-harmonic equations of the form $d^{\star} A(x, d \omega) =B(x,d\omega)$. Then, as an application of this local result, we prove a global $A_r$-weighted Poincaré inequality for functions that are solutions to such equations in John domains.

Article information

Source
Illinois J. Math., Volume 46, Number 1 (2002), 199-205.

Dates
First available in Project Euclid: 13 November 2009

Permanent link to this document
https://projecteuclid.org/euclid.ijm/1258136150

Digital Object Identifier
doi:10.1215/ijm/1258136150

Mathematical Reviews number (MathSciNet)
MR1936085

Zentralblatt MATH identifier
1071.35520

Subjects
Primary: 35J60: Nonlinear elliptic equations
Secondary: 31B05: Harmonic, subharmonic, superharmonic functions 46E35: Sobolev spaces and other spaces of "smooth" functions, embedding theorems, trace theorems 58A10: Differential forms

Citation

Ding, Shusen; Nolder, Craig A. Weighted Poincaré inequalities for solutions to $A$-harmonic equations. Illinois J. Math. 46 (2002), no. 1, 199--205. doi:10.1215/ijm/1258136150. https://projecteuclid.org/euclid.ijm/1258136150


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