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arXiv · 2010.00782

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

Sebastiano Don·Luca Lussardi·Andrea Pinamonti·Giulia Treu
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Abstract

We consider the functional $\int_\Omega g(\nabla u+\textbf X^\ast)d\mathscr L^{2n}$ where $g$ is convex and $\textbf X^\ast(x,y)=2(-y,x)$ 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.

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Sebastiano Don, Luca Lussardi, Andrea Pinamonti, Giulia Treu. 2020-10-01. Lipschitz minimizers for a class of integral functionals under the bounded slope condition. https://arxiv.org/abs/2010.00782

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