Minimizers of non convex scalar functionals and viscosity solutions of Hamilton-Jacobi equations

Zagatti, Sandro
April 2008
Calculus of Variations & Partial Differential Equations;Apr2008, Vol. 31 Issue 4, p511
Academic Journal
We consider a class of non convex scalar functionals of the form under standard assumptions of regularity of the solutions of the associated relaxed problem and of local affinity of the bipolar f ** of f on the set { f ** < f}. We provide an existence theorem, which extends known results to lagrangians depending explicitly on the three variables, by the introduction of integro-extremal minimizers of the relaxed functional which solve the equation or the opposite one, almost everywhere and in viscosity sense.


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