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On the dimension of...
On the dimension of p-harmonic measure in space
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Lewis, John L (författare)
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- Nyström, Kaj, 1969- (författare)
- Uppsala universitet,Analys och tillämpad matematik
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Vogel, Andrew (författare)
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(creator_code:org_t)
- 2013
- 2013
- Engelska.
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Ingår i: Journal of the European Mathematical Society (Print). - 1435-9855 .- 1435-9863. ; 15:6, s. 2197-2256
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https://doi.org/10.4...
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Abstract
Ämnesord
Stäng
- Let Omega subset of R-n, n >= 3, and let p, 1 < p < infinity, p not equal D 2, be given. In this paper we study the dimension of p-harmonic measures that arise from nonnegative solutions to the p-Laplace equation, vanishing on a portion of partial derivative Omega, in the setting of delta-Reifenberg flat domains. We prove, for p >= n, that there exists (delta) over tilde = (delta) over tilde (p, n) > 0 small such that if Omega is a delta-Reifenberg flat domain with delta < <(delta)over tilde>, then p-harmonic measure is concentrated on a set of sigma-finite Hn-1-measure. We prove, for p >= n, that for sufficiently flat Wolff snowflakes the Hausdorff dimension of p-harmonic measure is always less than n - 1. We also prove that if 2 < p < n, then there exist Wolff snowflakes such that the Hausdorff dimension of p-harmonic measure is less than n - 1, while if 1 < p < 2, then there exist Wolff snowflakes such that the Hausdorff dimension of p-harmonic measure is larger than n - 1. Furthermore, perturbing off the case p = 2; we derive estimates for the Hausdorff dimension of p-harmonic measure when p is near 2.
Ämnesord
- NATURVETENSKAP -- Matematik (hsv//swe)
- NATURAL SCIENCES -- Mathematics (hsv//eng)
Nyckelord
- p-harmonic function
- p-harmonic measure
- Hausdorff dimension
- Reifenberg flat domain
- Wolff snowflake
Publikations- och innehållstyp
- ref (ämneskategori)
- art (ämneskategori)
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