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We prove a boundary Harnack principle in Lipschitz domains with small constant for fully nonlinear and -Laplace-type equations with a right-hand side, as well as for the Laplace equation on nontangentially accessible domains under extra conditions. The approach is completely new and gives a systematic approach for proving similar results for a variety of equations and geometries.
@article{AIHPC_2023__40_1_133_0,
author = {Allen, Mark and Kriventsov, Dennis and Shahgholian, Henrik},
title = {The inhomogeneous boundary {Harnack} principle for fully nonlinear and $p${-Laplace} equations},
journal = {Annales de l'I.H.P. Analyse non lin\'eaire},
pages = {133--156},
volume = {40},
number = {1},
year = {2023},
doi = {10.4171/aihpc/40},
language = {EN},
url = {http://geodesic.mathdoc.fr/articles/10.4171/aihpc/40/}
}
TY - JOUR AU - Allen, Mark AU - Kriventsov, Dennis AU - Shahgholian, Henrik TI - The inhomogeneous boundary Harnack principle for fully nonlinear and $p$-Laplace equations JO - Annales de l'I.H.P. Analyse non linéaire PY - 2023 SP - 133 EP - 156 VL - 40 IS - 1 UR - http://geodesic.mathdoc.fr/articles/10.4171/aihpc/40/ DO - 10.4171/aihpc/40 LA - EN ID - AIHPC_2023__40_1_133_0 ER -
%0 Journal Article %A Allen, Mark %A Kriventsov, Dennis %A Shahgholian, Henrik %T The inhomogeneous boundary Harnack principle for fully nonlinear and $p$-Laplace equations %J Annales de l'I.H.P. Analyse non linéaire %D 2023 %P 133-156 %V 40 %N 1 %U http://geodesic.mathdoc.fr/articles/10.4171/aihpc/40/ %R 10.4171/aihpc/40 %G EN %F AIHPC_2023__40_1_133_0
Allen, Mark; Kriventsov, Dennis; Shahgholian, Henrik. The inhomogeneous boundary Harnack principle for fully nonlinear and $p$-Laplace equations. Annales de l'I.H.P. Analyse non linéaire, Tome 40 (2023) no. 1, pp. 133-156. doi: 10.4171/aihpc/40
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