Thumbnail - No thumbnail

Regularity Results for Eikonal-Type Equations with Nonsmooth Coefficients

Cannarsa, Piermarco; Cardaliaguet, Pierre (2012), Regularity Results for Eikonal-Type Equations with Nonsmooth Coefficients, NoDEA: Nonlinear Differential Equations and Applications, 19, 6, p. 751-769. http://dx.doi.org/10.1007/s00030-011-0150-1

Type
Article accepté pour publication ou publié
External document link
http://hal.archives-ouvertes.fr/hal-00578730/fr/
Date
2012
Journal name
NoDEA: Nonlinear Differential Equations and Applications
Volume
19
Number
6
Publisher
Springer
Pages
751-769
Publication identifier
Metadata
Show full item record
Author(s)
Cannarsa, Piermarco
Cardaliaguet, Pierre
Abstract (EN)
Solutions of the Hamilton-Jacobi equation $H(x,-Du(x))=1$, with $H(\cdot,p)$ Hölder continuous and $H(x,\cdot)$ convex and positively homogeneous of degree $1$, are shown to be locally semiconcave with a power-like modulus. An essential step of the proof is the ${\mathcal C}^{1,\alpha}$-regularity of the extremal trajectories associated with the multifunction generated by $D_pH$.
Subjects / Keywords
viscosity solutions; extremal trajectories; semiconcave functions; differential inclusions