Inversion des opérateurs non nécessairement linéaires et la connexion avec l’orthogonalité au sens de Birkoff-James et la notion de « nearness » au sens de Campanato.

par Michel Théra (Université de Limoges)

vendredi 17 janv. 2020, 11:00 → 12:00 Europe/Paris

XLIM Salle X.203

In this talk I will present  new invertibility theorems for non-necessary linear operators on a real Banach space, similar to the linear Cazassa-Christenses Lemma.  Such invertibility results go back to the so-called Neumann Lemma.

 

Our analysis benefits from the introduction of a new concept, strongly related to the Birkhoff-James orthogonality,  that is the notion of  near operator introduced  at the end of the eighties by Sergio Campanato in a series of papers, through which  he was able to unify  existence and regularity results for  PDE's and systems in non-divergence   based on the Schauder method, the Lax-Milgram theorem, the Cordes theorem and  the theory of monotone operators.