The boundary Harnack inequality for variable exponent \(p\) -Laplacian, Carles

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• 作者：Tomasz Adamowicz ; Niklas L. P. Lundström
• 关键词：Ball condition ; Boundary Harnack inequality ; Harmonic measure ; NTA domain ; Nonstandard growth equation ; p ; harmonic
• 刊名：Annali di Matematica Pura ed Applicata
• 出版年：2016
• 出版时间：April 2016
• 年：2016
• 卷：195
• 期：2
• 页码：623-658
• 全文大小：792 KB
• 刊物类别：Mathematics and Statistics
• 刊物主题：Mathematics
  Mathematics
  
• 出版者：Springer Berlin / Heidelberg
• ISSN：1618-1891

文摘

We investigate various boundary decay estimates for \({p(\cdot )}\)-harmonic functions. For domains in \({\mathbb {R}}^n, n\ge 2\) 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.