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Remarks on some minimization problems associated with BV norms

This research was partially supported by NSF.
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  • The purpose of this paper is twofold. Firstly I present an optimal regularity result for minimizers of a $ 1D $ convex functional involving the BV-norm, under Neumann boundary condition. This functional is a simplified version of models occuring in Image Processing. Secondly I investigate the existence of minimizers for the same functional under Dirichlet boundary condition. Surprisingly, this turns out to be a delicate issue, which is still widely open.

    Mathematics Subject Classification: Primary: 26A45, 35J20; Secondary: 35J25.


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