Lipschitz minimizers for a class of integral functionals under the bounded slope condition. (March 2022) - Don, Sebastiano; Lussardi, Luca; Pinamonti, Andrea; Treu, Giulia
Abstract: We consider the functional ∫ Ω g ( ∇ u + X ∗ ) d L 2 n where g is convex and X ∗ ( x, y ) = 2 ( − y, x ) and we study the minimizers in BV ( Ω ) of the associated Dirichlet problem. We prove that, under the bounded slope condition on the boundary datum, and suitable conditions on g, there exists a unique minimizer which is also Lipschitz continuous. The assumptions on g allow to consider both the case with superlinear growth and the one with linear growth. Moreover neither uniform ellipticity nor smoothness of g are assumed.