A note on the regularity of solutions of Hamilton-Jacobi equations with superlinear growth in the gradient variable

Pierre Cardaliaguet

ESAIM: Control, Optimisation and Calculus of Variations (2009)

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

Abstract

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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.

How to cite

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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 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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  1. [1] M. Bardi and I. Capuzzo Dolcetta, Optimal control and viscosity solutions of Hamilton-Jacobi-Bellman equations. Birkhäuser (1996). Zbl0890.49011MR1484411
  2. [2] G. Barles, Regularity results for first order Hamilton-Jacobi equations. Differ. Integral Equ. 3 (1990) 103–125. Zbl0739.35012MR1014729
  3. [3] G. Barles, Solutions de viscosité des équations de Hamilton-Jacobi. Springer-Verlag, Berlin (1994). Zbl0819.35002MR1613876
  4. [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. [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. [6] P.-L. Lions, Regularizing effects for first-order Hamilton-Jacobi equations. Applicable Anal. 20 (1985) 283–307. Zbl0551.35014MR814955
  7. [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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