Smooth Variational Principles and non Smooth Analysis in Banach Spaces

Abstract

Variational principles are well established tools to deal with minimization problems without compactness. We present here recent developments on smooth variational principles. In particular, we show how the smooth variational principle of R. Deville, G. Godefroy and V. Zizler allows to develop a differential calculus for non smooth functions in smooth Banach spaces. This calculus is useful for solving Hamilton-Jacobi equations in infinite dimensions since the “right” solutions of these equations are usually not smooth.