We consider a parabolic equation driven by a nonlinear diffusive operator and we obtain a gradient estimate in the domain where the equation takes place. This estimate depends on the structural constants of the equation, on the geometry of the ambient space and on the initial and boundary data. As a byproduct, one easily obtains a universal interior estimate, not depending on the parabolic data. The setting taken into account includes sourcing terms and general diffusion coefficients. The results are new, to the best of our knowledge, even in the Euclidean setting, though we treat here also the case of a complete Riemannian manifold.
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Keywords: Parabolic equations on Riemannian manifolds, maximum principle, global gradient estimates
@article{COCV_2021__27_1_A23_0,
author = {Dipierro, Serena and Gao, Zu and Valdinoci, Enrico},
title = {Global gradient estimates for nonlinear parabolic operators},
journal = {ESAIM: Control, Optimisation and Calculus of Variations},
year = {2021},
publisher = {EDP-Sciences},
volume = {27},
doi = {10.1051/cocv/2021016},
language = {en},
url = {https://www.numdam.org/articles/10.1051/cocv/2021016/}
}
TY - JOUR AU - Dipierro, Serena AU - Gao, Zu AU - Valdinoci, Enrico TI - Global gradient estimates for nonlinear parabolic operators JO - ESAIM: Control, Optimisation and Calculus of Variations PY - 2021 VL - 27 PB - EDP-Sciences UR - https://www.numdam.org/articles/10.1051/cocv/2021016/ DO - 10.1051/cocv/2021016 LA - en ID - COCV_2021__27_1_A23_0 ER -
%0 Journal Article %A Dipierro, Serena %A Gao, Zu %A Valdinoci, Enrico %T Global gradient estimates for nonlinear parabolic operators %J ESAIM: Control, Optimisation and Calculus of Variations %D 2021 %V 27 %I EDP-Sciences %U https://www.numdam.org/articles/10.1051/cocv/2021016/ %R 10.1051/cocv/2021016 %G en %F COCV_2021__27_1_A23_0
Dipierro, Serena; Gao, Zu; Valdinoci, Enrico. Global gradient estimates for nonlinear parabolic operators. ESAIM: Control, Optimisation and Calculus of Variations, Tome 27 (2021), article no. 21. doi: 10.1051/cocv/2021016
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