We prove the existence of a global Lipschitz minimizer of functionals of the form I (u) = \int \Omega f(\nabla u(x)) + g(x, u(x)) dx, u \in \phi + W1,1 0 (\Omega ), assuming that \phi satisfies the bounded slope condition (BSC). Our assumptions on the Lagrangian allow the function f to be strongly degenerate.
ON THE LIPSCHITZ REGULARITY FOR MINIMA OF FUNCTIONALS DEPENDING ON x, u, AND ∇u UNDER THE BOUNDED SLOPE CONDITION
Treu G.
2022
Abstract
We prove the existence of a global Lipschitz minimizer of functionals of the form I (u) = \int \Omega f(\nabla u(x)) + g(x, u(x)) dx, u \in \phi + W1,1 0 (\Omega ), assuming that \phi satisfies the bounded slope condition (BSC). Our assumptions on the Lagrangian allow the function f to be strongly degenerate.
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