We consider a class of non convex scalar functionals of the form F(u) = ∫Ω f(x,u,Du)dx, 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 f** (x, u,Du) - f(x, u,Du) =0, or the opposite one, almost everywhere and in viscosity sense. © 2007 Springer-Verlag.
Minimizers of non convex scalar functionals and viscosity solutions of Hamilton-Jacobi equations / Zagatti, Sandro. - In: CALCULUS OF VARIATIONS AND PARTIAL DIFFERENTIAL EQUATIONS. - ISSN 0944-2669. - 31:4(2008), pp. 511-519. [10.1007/s00526-007-0124-7]
Minimizers of non convex scalar functionals and viscosity solutions of Hamilton-Jacobi equations
Zagatti, Sandro
2008-01-01
Abstract
We consider a class of non convex scalar functionals of the form F(u) = ∫Ω f(x,u,Du)dx, 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 f** (x, u,Du) - f(x, u,Du) =0, or the opposite one, almost everywhere and in viscosity sense. © 2007 Springer-Verlag.File | Dimensione | Formato | |
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