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We investigate the regularity of solutions of first order Hamilton-Jacobi equation with super linear growth in the gradient variable. We show that the solutions are locally Hölder continuous with Hölder exponent depending only on the growth of the hamiltonian. The proof relies on a reverse Hölder inequality.
@article{COCV_2009__15_2_367_0,
author = {Cardaliaguet, Pierre},
title = {A note on the regularity of solutions of {Hamilton-Jacobi} equations with superlinear growth in the gradient variable},
journal = {ESAIM: Control, Optimisation and Calculus of Variations},
pages = {367--376},
publisher = {EDP-Sciences},
volume = {15},
number = {2},
year = {2009},
doi = {10.1051/cocv:2008028},
mrnumber = {2513090},
zbl = {1175.35030},
language = {en},
url = {http://geodesic.mathdoc.fr/articles/10.1051/cocv:2008028/}
}
TY - JOUR AU - Cardaliaguet, Pierre TI - A note on the regularity of solutions of Hamilton-Jacobi equations with superlinear growth in the gradient variable JO - ESAIM: Control, Optimisation and Calculus of Variations PY - 2009 SP - 367 EP - 376 VL - 15 IS - 2 PB - EDP-Sciences UR - http://geodesic.mathdoc.fr/articles/10.1051/cocv:2008028/ DO - 10.1051/cocv:2008028 LA - en ID - COCV_2009__15_2_367_0 ER -
%0 Journal Article %A Cardaliaguet, Pierre %T A note on the regularity of solutions of Hamilton-Jacobi equations with superlinear growth in the gradient variable %J ESAIM: Control, Optimisation and Calculus of Variations %D 2009 %P 367-376 %V 15 %N 2 %I EDP-Sciences %U http://geodesic.mathdoc.fr/articles/10.1051/cocv:2008028/ %R 10.1051/cocv:2008028 %G en %F COCV_2009__15_2_367_0
Cardaliaguet, Pierre. A note on the regularity of solutions of Hamilton-Jacobi equations with superlinear growth in the gradient variable. ESAIM: Control, Optimisation and Calculus of Variations, Tome 15 (2009) no. 2, pp. 367-376. doi: 10.1051/cocv:2008028
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