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

Adamowicz, Tomasz (author): Institute of Mathematics of the Polish Academy of Sciences, Warsaw, Poland

Lundström, Niklas L.P. 1980- (author): Umeå universitet,Institutionen för matematik och matematisk statistik

(creator_code:org_t)

2015-02-20
2016
English.
In: Annali di Matematica Pura ed Applicata. - : Springer. - 0373-3114 .- 1618-1891. ; 195:2, s. 623-658

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Abstract Subject headings

We investigate various boundary decay estimates for p(⋅)-harmonic functions. For domains in Rn,n≥2satisfying the ball condition (C1,1-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.

About the subject

NATURAL SCIENCES: NATURAL SCIENCES; and Mathematics; and Mathematical Ana ...

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