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 publiéExternal document link
http://hal.archives-ouvertes.fr/hal-00578730/fr/Date
2012Journal name
NoDEA: Nonlinear Differential Equations and ApplicationsVolume
19Number
6Publisher
Springer
Pages
751-769
Publication identifier
Metadata
Show full item recordAbstract (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 inclusionsRelated items
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