On a theorem of existence and uniqueness for the elastostatics of a non linear dielectric

Abstract

In this paper we shall prove a theorem of existence and uniqueness of the solution for the equilibrium equations of a non linear elastic dielectric, provided that for the connected linear problem an existence and uniqueness theorem is valid. To this purpose we shall apply a functional analysis method which has been previously used by Van Buren [1] and Stoppelli [2] for a non linear elastic system.The underneath scheme will be the continuum-elastic one.