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Quasi-linear PDEs and low-dimensional sets
University of Kentucky, Lexington, KY, USA.
Uppsala University, Disciplinary Domain of Science and Technology, Mathematics and Computer Science, Department of Mathematics, Analysis and Probability Theory.
2015 (English)In: Journal of the European Mathematical Society (Print), ISSN 1435-9855, E-ISSN 1435-9863Article in journal (Refereed) Accepted
Abstract [en]

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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URN: urn:nbn:se:uu:diva-260772OAI: diva2:848388
Available from: 2015-08-24 Created: 2015-08-24 Last updated: 2016-03-01

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