# 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 (2009)

- Volume: 15, Issue: 2, page 367-376
- ISSN: 1292-8119

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topCardaliaguet, 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 15.2 (2009): 367-376. <http://eudml.org/doc/245138>.

@article{Cardaliaguet2009,

abstract = {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.},

author = {Cardaliaguet, Pierre},

journal = {ESAIM: Control, Optimisation and Calculus of Variations},

keywords = {Hamilton-Jacobi equation; viscosity solutions; optimal control; regularity; reverse Hölder inequality; Hamilton-Jacobi equations; regularity of solutions},

language = {eng},

number = {2},

pages = {367-376},

publisher = {EDP-Sciences},

title = {A note on the regularity of solutions of Hamilton-Jacobi equations with superlinear growth in the gradient variable},

url = {http://eudml.org/doc/245138},

volume = {15},

year = {2009},

}

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

PB - EDP-Sciences

VL - 15

IS - 2

SP - 367

EP - 376

AB - 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.

LA - eng

KW - Hamilton-Jacobi equation; viscosity solutions; optimal control; regularity; reverse Hölder inequality; Hamilton-Jacobi equations; regularity of solutions

UR - http://eudml.org/doc/245138

ER -

## References

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- [2] G. Barles, Regularity results for first order Hamilton-Jacobi equations. Differ. Integral Equ. 3 (1990) 103–125. Zbl0739.35012MR1014729
- [3] G. Barles, Solutions de viscosité des équations de Hamilton-Jacobi. Springer-Verlag, Berlin (1994). Zbl0819.35002MR1613876
- [4] A. Bensoussan and J. Frehse, Regularity results for nonlinear elliptic systems and applications, Applied Mathematical Sciences 151. Springer-Verlag, Berlin (2002). Zbl1055.35002MR1917320
- [5] F.W. Gehring, The ${L}^{p}$-integrability of the partial derivatives of a quasiconformal mapping. Acta Math. 130 (1973) 265–277. Zbl0258.30021MR402038
- [6] P.-L. Lions, Regularizing effects for first-order Hamilton-Jacobi equations. Applicable Anal. 20 (1985) 283–307. Zbl0551.35014MR814955
- [7] F. Rampazzo and C. Sartori, Hamilton-Jacobi-Bellman equations with fast gradient-dependence. Indiana Univ. Math. J. 49 (2000) 1043–1077. Zbl0987.35024MR1803221

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