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Quasi-linear PDEs a...
Quasi-linear PDEs and low-dimensional sets
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- Lewis, John L. (författare)
- University of Kentucky, Lexington, KY, USA
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- Nyström, Kaj, 1969- (författare)
- Uppsala universitet,Analys och sannolikhetsteori
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(creator_code:org_t)
- 2018
- 2018
- Engelska.
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Ingår i: Journal of the European Mathematical Society (Print). - 1435-9855 .- 1435-9863. ; 20:7, s. 1689-1746
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https://urn.kb.se/re...
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https://doi.org/10.4...
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Abstract
Ämnesord
Stäng
- 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.
Ämnesord
- NATURVETENSKAP -- Matematik -- Matematisk analys (hsv//swe)
- NATURAL SCIENCES -- Mathematics -- Mathematical Analysis (hsv//eng)
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