Geodesic
Quasi-linear PDEs and low-dimensional sets
Journal of the European Mathematical Society, Tome 20 (2018) no. 7, pp. 1689-1746.

Voir la notice de l'article provenant de la source EMS Press

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 Σ in Rn and this is different compared to the more traditional setting of boundary value problems set in the geometrical situation of a bounded domain in Rn 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.
DOI : 10.4171/jems/797
Classification : 35-XX, 31-XX
Mots-clés : Boundary Harnack inequality, p-harmonic function, A-harmonic function, variable coefficients, Reifenberg flat domain, low-dimensional sets, Martin boundary 
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     title = {Quasi-linear {PDEs} and low-dimensional sets},
     journal = {Journal of the European Mathematical Society},
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     doi = {10.4171/jems/797},
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John L. Lewis; Kaj Nyström. Quasi-linear PDEs and low-dimensional sets. Journal of the European Mathematical Society, Tome 20 (2018) no. 7, pp. 1689-1746. doi : 10.4171/jems/797. https://geodesic-test.mathdoc.fr/articles/10.4171/jems/797/

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