Seminarium "The Trans-Carpathian Seminar on Geometry & Physics"

Hyperbolicity of a system of partial differential equations refers tocertain essentially algebraic conditions, on the other hand such a systemshould have properties like the wave equation, basically it should possessthe domain of dependence property. Starting with a brief exposition ofbasic concepts related to the action principle of the theory of mapsbetween manifolds we will sketch the proof of the domain of dependencetheorem (Christodoulou) for systems of the Euler-Lagrange equationssatisfying certain regular hyperbolicity condition. This modern notionrefers strictly to Lagrangians and it is applicable to systems which cannotsatisfy classical notions of hyperbolicity (Leray, Friedrichs).