Jason TridonLMAP
Le 30 avr. 2026
Titre: Determination of functions in non-bounded domains with epsilon-cone condition
Résumé: We study the problem of unique function determination: if two functions f and g satisfy ∣∇f∣=∣∇g∣, do we necessarily have f=g up to an additive constant? Here, the norm of the gradient can be understood in the sense of the local slope à la De Giorgi. When the space is bounded, the answer is known to be positive. For a general Hilbert space, it has been shown that the convexity of both functions and information on the so-called Crandall-Pazy direction provide sufficient conditions to give a positive answer. In this talk, we present the notion of unique function determination and explain how the epsilon-cone condition can be used to relax the convexity assumption.