The boundary Harnack inequality for variable exponent p-Laplacian, Carleson estimates, barrier functions and p(⋅)-harmonic measures

2014/05/12 by Tomasz Adamowicz, Adamowicz, Tomasz, Niklas L. P. Lundström +2
Mathematics · #Advanced Harmonic Analysis Research #Advanced Mathematical Physics Problems #Nonlinear Partial Differential Equations #math.AP #msc:31B25 #msc:31B52 #msc:35B09 #msc:35J92

paper · pdf · doi:10.48550/arxiv.1405.2678

31 pages, 1 figure

arxiv created 2014/05/12 · arxiv updated 2014/05/13

Abstract

We investigate various boundary decay estimates for p(⋅)-harmonic functions. For domains in ℝⁿ, n≥ 2 satisfying the ball condition (C^1,1-domains) we show the boundary Harnack inequality for p(⋅)-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(⋅)-harmonic functions in NTA domains in ℝⁿ and provide lower- and upper- growth estimates and a doubling property for a p(⋅)-harmonic measure.

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