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 
@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://archive.numdam.org/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://archive.numdam.org/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://archive.numdam.org/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. http://archive.numdam.org/articles/10.1051/cocv:2008028/

[1] M. Bardi and I. Capuzzo Dolcetta, Optimal control and viscosity solutions of Hamilton-Jacobi-Bellman equations. Birkhäuser (1996). | MR | Zbl

[2] G. Barles, Regularity results for first order Hamilton-Jacobi equations. Differ. Integral Equ. 3 (1990) 103-125. | MR | Zbl

[3] G. Barles, Solutions de viscosité des équations de Hamilton-Jacobi. Springer-Verlag, Berlin (1994). | MR | Zbl

[4] A. Bensoussan and J. Frehse, Regularity results for nonlinear elliptic systems and applications, Applied Mathematical Sciences 151. Springer-Verlag, Berlin (2002). | MR | Zbl

[5] F.W. Gehring, The L p -integrability of the partial derivatives of a quasiconformal mapping. Acta Math. 130 (1973) 265-277. | MR | Zbl

[6] P.-L. Lions, Regularizing effects for first-order Hamilton-Jacobi equations. Applicable Anal. 20 (1985) 283-307. | MR | Zbl

[7] F. Rampazzo and C. Sartori, Hamilton-Jacobi-Bellman equations with fast gradient-dependence. Indiana Univ. Math. J. 49 (2000) 1043-1077. | MR | Zbl

Cité par Sources :