In this article we prove the existence of strong minimizers for Blake & Zisserman’s functional under Dirichlet boundary condition. The result is obtained by showing partial regularity of weak solutions up to the boundary through blow-up techniques and decay properties for bi-harmonic functions in the half-disk. This research is also motivated by the possibility of studying variational formulation of the inpainting problem for 2-dimensional images which are locally damaged and its approximation via the variational convergence introduced and studied by E. De Giorgi.

A Dirichlet problem with free gradient discontinuity

CARRIERO, Michele;LEACI, Antonio;
2010-01-01

Abstract

In this article we prove the existence of strong minimizers for Blake & Zisserman’s functional under Dirichlet boundary condition. The result is obtained by showing partial regularity of weak solutions up to the boundary through blow-up techniques and decay properties for bi-harmonic functions in the half-disk. This research is also motivated by the possibility of studying variational formulation of the inpainting problem for 2-dimensional images which are locally damaged and its approximation via the variational convergence introduced and studied by E. De Giorgi.
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Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/11587/354673
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