Bridges between several notions of viscosity solutions in P2(Rd)
speaker: Chloé Jimenez (Université de Bretagne Occidentale)abstract: After presenting the notion of Lions' derivative in the Wasserstein space, I will present several de nitions of viscosity solutions for Hamilton Jacobi equations in P2(Rd). One of them was introduced by Gangbo, Nguyen and Tudorascu (GNT), the second one by Lions. I will show that both use very natural subdi erentials. Owing to de ne also GNT solutions using test functions, I will talk about the de nition of strict viscosity solutions which appeared in the work of Marigonda and Quincampoix (MQ). Then we will see an equivalence result between the points of view of GNT and MQ and build a bridge with Lions' de nition that preserve regularity of the Hamiltonian. During the talk, a surprising link will also appear with the enlightening book of Ambrosio, Gigli and Savare, precursors of Lions' derivative.
timetable:
Thu 5 Dec, 12:00 - 12:45, Aula Dini
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