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The boundary Harnack inequality for variable exponent $p$-Laplacian, Carleson estimates, barrier functions and $p(\cdot)$-harmonic measures
- Publication Year :
- 2014
-
Abstract
- We investigate various boundary decay estimates for $p(\cdot)$-harmonic functions. For domains in $\mathbb{R}^n, n\geq 2$ satisfying the ball condition ($C^{1,1}$-domains) we show the boundary Harnack inequality for $p(\cdot)$-harmonic functions under the assumption that the variable exponent $p$ is a bounded Lipschitz function. The proof involves barrier functions and chaining arguments. Moreover, we prove a Carleson type estimate for $p(\cdot)$-harmonic functions in NTA domains in $\mathbb{R}^n$ and provide lower- and upper- growth estimates and a doubling property for a $p(\cdot)$-harmonic measure.<br />Comment: 31 pages, 1 figure
- Subjects :
- Mathematics - Analysis of PDEs
31B52 (Primary), 35J92, 35B09, 31B25 (Secondary)
Subjects
Details
- Database :
- arXiv
- Publication Type :
- Report
- Accession number :
- edsarx.1405.2678
- Document Type :
- Working Paper