On p-harmonic measures in half-spaces

José G. Llorente; Juan J. Manfredi; William C. Troy; Jang Mei Wu

doi:10.1007/s10231-018-00822-9

On p-harmonic measures in half-spaces

José G. Llorente, Juan J. Manfredi, William C. Troy, Jang Mei Wu

Mathematics

Research output: Contribution to journal › Article › peer-review

Abstract

For all 1 < p< ∞ and N≥ 2 we prove by using ODE shooting techniques that there is a constant α(p, N) > 0 such that the p-harmonic measure in R+N of a ball of radius 0 < δ≤ 1 in R^N ^- ¹ is bounded above and below by a constant times δ^α ⁽ ^p ^. ^N ⁾. We provide explicit estimates for the exponent α(p, N).

Original language	English (US)
Pages (from-to)	1381-1405
Number of pages	25
Journal	Annali di Matematica Pura ed Applicata
Volume	198
Issue number	4
DOIs	https://doi.org/10.1007/s10231-018-00822-9
State	Published - Aug 1 2019

Keywords

Shooting method
p-Harmonic measure
p-Laplacian

ASJC Scopus subject areas

Applied Mathematics

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10.1007/s10231-018-00822-9

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AU - Manfredi, Juan J.

AU - Troy, William C.

AU - Wu, Jang Mei

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Y1 - 2019/8/1

N2 - For all 1 < p< ∞ and N≥ 2 we prove by using ODE shooting techniques that there is a constant α(p, N) > 0 such that the p-harmonic measure in R+N of a ball of radius 0 < δ≤ 1 in RN - 1 is bounded above and below by a constant times δα ( p . N ). We provide explicit estimates for the exponent α(p, N).

AB - For all 1 < p< ∞ and N≥ 2 we prove by using ODE shooting techniques that there is a constant α(p, N) > 0 such that the p-harmonic measure in R+N of a ball of radius 0 < δ≤ 1 in RN - 1 is bounded above and below by a constant times δα ( p . N ). We provide explicit estimates for the exponent α(p, N).

KW - Shooting method

KW - p-Harmonic measure

KW - p-Laplacian

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On p-harmonic measures in half-spaces

Abstract

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