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Article Dans Une Revue Journal of Geometric Analysis Année : 2024

VISCOSITY SOLUTIONS OF HAMILTON-JACOBI EQUATIONS IN PROPER CAT(0) SPACES

Résumé

In this article, we develop a novel notion of viscosity solutions for first order Hamilton-Jacobi equations in proper CAT(0) spaces. The notion of viscosity is defined by taking test functions that are directionally differentiable and can be represented as a difference of two semiconvex functions. Under mild assumptions on the Hamiltonian, we recover the main features of viscosity theory for both the stationary and the time-dependent cases in this setting: the comparison principle and Perron's method. Finally, we show that this notion of viscosity coincides with classical one in R N and we give several examples of Hamilton-Jacobi equations in more general CAT(0) spaces covered by this setting.
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Dates et versions

hal-03899199 , version 1 (14-12-2022)

Identifiants

Citer

Othmane Jerhaoui, Hasnaa Zidani. VISCOSITY SOLUTIONS OF HAMILTON-JACOBI EQUATIONS IN PROPER CAT(0) SPACES. Journal of Geometric Analysis, 2024, 34 (2), pp.53. ⟨10.1007/s12220-023-01484-7⟩. ⟨hal-03899199⟩
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