Papers
Topics
Authors
Recent
Gemini 2.5 Flash
Gemini 2.5 Flash
173 tokens/sec
GPT-4o
7 tokens/sec
Gemini 2.5 Pro Pro
46 tokens/sec
o3 Pro
4 tokens/sec
GPT-4.1 Pro
38 tokens/sec
DeepSeek R1 via Azure Pro
28 tokens/sec
2000 character limit reached

The boundary Harnack inequality for variable exponent $p$-Laplacian, Carleson estimates, barrier functions and $p(\cdot)$-harmonic measures (1405.2678v1)

Published 12 May 2014 in math.AP

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.

Summary

We haven't generated a summary for this paper yet.