Geodesic
Weak comparison principles for fully nonlinear degenerate parabolic equations with discontinuous source terms
Minimax theory and its applications, Tome 8 (2023) no. 1
Cet article a éte moissonné depuis la source Minimax Theory and its Applications website

Voir la notice de l'article

We study the initial value problem for a fully nonlinear degenerate parabolic equation with discontinuous source terms, to which a usual type of comparison principles does not apply. Examples include singular equations appearing in surface evolution problems such as the level-set mean curvature flow equation with a driving force term and a discontinuous source term. By a suitable scaling, we establish weak comparison principles for a viscosity sub- and supersolution to the equation. We also present uniqueness and existence results of possibly discontinuous viscosity solutions.
Mots-clés : Weak comparison principle, viscosity solution, fully nonlinear equation, discontinuous source term, level-set mean curvature flow equation 
@article{MTA_2023_8_1_a1,
     author = {Nao Hamamuki and Kuniyasu Misu},
     title = {Weak comparison principles for fully nonlinear degenerate parabolic equations with discontinuous source terms},
     journal = {Minimax theory and its applications},
     year = {2023},
     volume = {8},
     number = {1},
     zbl = {1514.35071},
     url = {http://geodesic.mathdoc.fr/item/MTA_2023_8_1_a1/}
}
TY  - JOUR
AU  - Nao Hamamuki
AU  - Kuniyasu Misu
TI  - Weak comparison principles for fully nonlinear degenerate parabolic equations with discontinuous source terms
JO  - Minimax theory and its applications
PY  - 2023
VL  - 8
IS  - 1
UR  - http://geodesic.mathdoc.fr/item/MTA_2023_8_1_a1/
ID  - MTA_2023_8_1_a1
ER  - 
%0 Journal Article
%A Nao Hamamuki
%A Kuniyasu Misu
%T Weak comparison principles for fully nonlinear degenerate parabolic equations with discontinuous source terms
%J Minimax theory and its applications
%D 2023
%V 8
%N 1
%U http://geodesic.mathdoc.fr/item/MTA_2023_8_1_a1/
%F MTA_2023_8_1_a1
Nao Hamamuki; Kuniyasu Misu. Weak comparison principles for fully nonlinear degenerate parabolic equations with discontinuous source terms. Minimax theory and its applications, Tome 8 (2023) no. 1. http://geodesic.mathdoc.fr/item/MTA_2023_8_1_a1/