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Regularity Results for Eikonal-Type Equations with Nonsmooth Coefficients

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Date
2012
Link to item file
http://hal.archives-ouvertes.fr/hal-00578730/fr/
Dewey
Probabilités et mathématiques appliquées
Sujet
viscosity solutions; extremal trajectories; semiconcave functions; differential inclusions
Journal issue
NoDEA: Nonlinear Differential Equations and Applications
Volume
19
Number
6
Publication date
2012
Article pages
751-769
Publisher
Springer
DOI
http://dx.doi.org/10.1007/s00030-011-0150-1
URI
https://basepub.dauphine.fr/handle/123456789/5985
Collections
  • CEREMADE : Publications
Metadata
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Author
Cannarsa, Piermarco
Cardaliaguet, Pierre
Type
Article accepté pour publication ou publié
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 $D_pH$.

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