Relaxation of Nonlocal Singular Integrals

ABSTRACT

In this paper we study well-posedness of a class of nonconvex variational principles arising in regularization theory for denoising of data with sampling errors and level set regularization methods for inverse problems. These models result in minimization of nonconvex, singular functionals involving (possibly) non-local operators.

Keywords:

• Multiple integrals
• Quasi-convexity
• Relaxation

Mathematics Subject Classification:

• 47A52
• 49J45

ACKNOWLEDGMENT

The work of the authors is supported by FWF (Austrian Science Fund) Project Y-123INF and P-15617.