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Session S02 - Diverse Aspects of Elliptic PDEs and Related Problems

Wednesday, July 21, 19:00 ~ 19:30 UTC-3

A viscosity solution approach to regularity properties of the optimal value function

Pablo Ochoa

CONICET-Universidad Nacional de Cuyo, Argentina   -   This email address is being protected from spambots. You need JavaScript enabled to view it.

In this paper, we analyze the optimal value function $v$ associated to a general parametric optimization problem via the theory of viscosity solutions. The novelty is that we obtain regularity properties of $v$ by showing that it is a viscosity solution to a set of first-order equations. As a consequence, in Banach spaces, we provide sufficient conditions for local and global Lipschitz properties of $v$. We also derive, in finite dimensions, conditions for optimality through a comparison principle. Finally, we study the relationship between viscosity and Clarke generalized solutions to get further differentiability properties of $v$ in Euclidean spaces.

Joint work with Virginia N. Vera de Serio (Universidad Nacional de Cuyo, Argentina).

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