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.

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.

DOI : 10.1051/cocv:2008028
Classification : 35F20, 49L25
Mots-clés : Hamilton-Jacobi equation, viscosity solutions, optimal control, regularity, reverse Hölder inequality 
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     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://www.numdam.org/articles/10.1051/cocv:2008028/}
}
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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. http://www.numdam.org/articles/10.1051/cocv:2008028/

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