Hamilton-Jacobi equations in infinite dimensions. I: Uniqueness of viscosity solutions
In a series of previous papers the authors have introduced the concept of viscosity solutions for Hamilton-Jacobi equations in \({\mathbb{R}}^ n\) of the form \(H(x,u,Du)=0\) and proved existence and uniqueness for a large class of Hamiltonian functions H. This is a first work of a series of papers where the authors extend their beautiful theory to infinite dimensional Banach spaces with the Radon-Nikodym property. The main result of this paper is a uniqueness theorem of viscosity solutions under appropriate conditions on H which resemble those from the finite dimensional case. A key ingredient of the uniqueness in the infinite dimensional setting is Stegall's variational principle.
infinite dimensional Banach spaces with the Radon-Nikodym property
scientific article; zbMATH DE number 4019853
scientific article