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Träfflista för sökning "L773:1435 9855 ;pers:(Lewis John L.)"

Sökning: L773:1435 9855 > Lewis John L.

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1.
  • Lewis, John L, et al. (författare)
  • On the dimension of p-harmonic measure in space
  • 2013
  • Ingår i: Journal of the European Mathematical Society (Print). - 1435-9855 .- 1435-9863. ; 15:6, s. 2197-2256
  • Tidskriftsartikel (refereegranskat)abstract
    • 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.
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2.
  • Lewis, John L., et al. (författare)
  • Quasi-linear PDEs and low-dimensional sets
  • 2018
  • Ingår i: Journal of the European Mathematical Society (Print). - 1435-9855 .- 1435-9863. ; 20:7, s. 1689-1746
  • Tidskriftsartikel (refereegranskat)abstract
    • In this paper we establish new results concerning boundary Harnack inequalities and the Martin boundary problem, for non-negative solutions to equations of $p$-Laplace type with variable coefficients. The key novelty is that we consider solutions which vanish only on a low-dimensional set $\Sigma$ in $\mathbb R^n$ and this is different compared to the more traditional setting of boundary value problems set in the geometrical situation of a bounded domain in $\mathbb R^n$ having a boundary with (Hausdorff) dimension in the range $[n-1,n)$. We establish our  quantitative and scale-invariant estimates in the context of low-dimensional Reifenberg flat sets.
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  • Resultat 1-2 av 2
Typ av publikation
tidskriftsartikel (2)
Typ av innehåll
refereegranskat (2)
Författare/redaktör
Nyström, Kaj, 1969- (2)
Lewis, John L. (2)Ta bort avgränsningen
Vogel, Andrew (1)
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Uppsala universitet (2)
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Engelska (2)
Forskningsämne (UKÄ/SCB)
Naturvetenskap (2)

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