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Article Dans Une Revue Nonlinear Differential Equations and Applications Année : 2012

Regularity Results for Eikonal-Type Equations with Nonsmooth Coefficients

Résumé

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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Dates et versions

hal-00578730 , version 1 (22-03-2011)

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Piermarco Cannarsa, Pierre Cardaliaguet. Regularity Results for Eikonal-Type Equations with Nonsmooth Coefficients. Nonlinear Differential Equations and Applications, 2012, 19 (6), pp.751--769. ⟨hal-00578730⟩
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