A Generalization of the lasry-lions method for functions in reflexive banach spaces

Abstract

The Lasry–Lions regularization method is extended to arbitrary functions in reflexive Banach spaces The regularization effect of the method arises from the Fréchet-differentiability of the conjugate f _∗ for an uniformly convex function f in a reflexive Banach space By means of Toland s and Singers duality theory one can derive the first and second regularization of an arbitrary function in a natural way

Keywords:

• Moreau-Yosida Approximation
• Regularization Approximation
• D c Functions
• Duality Theory of Toland and Singer