Lipschitz minimizers for a class of integral functionals under the bounded slope condition

Abstract

We consider the functional ${\int }_{\Omega }g(\nabla u+{\text{X}}^{\ast })d{\mathcal{L}}^{2n}$ where $g$ is convex and ${\text{X}}^{\ast }(x,y)=2(-y,x)$ and we study the minimizers in $BV(\Omega )$ 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.

35 pages. arXiv admin note: text overlap with arXiv:1307.4442