Geodesic
Quasi-linear PDEs and low-dimensional sets
Journal of the European Mathematical Society, Tome 20 (2018) no. 7, pp. 1689-1746 Cet article a éte moissonné depuis la source EMS Press

Voir la notice de l'article

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
Keywords: Boundary Harnack inequality, p-harmonic function, A-harmonic function, variable coefficients, Reifenberg flat domain, low-dimensional sets, Martin boundary 
@article{JEMS_2018_20_7_a4,
     author = {John L. Lewis and Kaj Nystr\"om},
     title = {Quasi-linear {PDEs} and low-dimensional sets},
     journal = {Journal of the European Mathematical Society},
     pages = {1689--1746},
     year = {2018},
     volume = {20},
     number = {7},
     doi = {10.4171/jems/797},
     url = {http://geodesic.mathdoc.fr/articles/10.4171/jems/797/}
}
TY  - JOUR
AU  - John L. Lewis
AU  - Kaj Nyström
TI  - Quasi-linear PDEs and low-dimensional sets
JO  - Journal of the European Mathematical Society
PY  - 2018
SP  - 1689
EP  - 1746
VL  - 20
IS  - 7
UR  - http://geodesic.mathdoc.fr/articles/10.4171/jems/797/
DO  - 10.4171/jems/797
ID  - JEMS_2018_20_7_a4
ER  - 
%0 Journal Article
%A John L. Lewis
%A Kaj Nyström
%T Quasi-linear PDEs and low-dimensional sets
%J Journal of the European Mathematical Society
%D 2018
%P 1689-1746
%V 20
%N 7
%U http://geodesic.mathdoc.fr/articles/10.4171/jems/797/
%R 10.4171/jems/797
%F JEMS_2018_20_7_a4
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

Cité par Sources :