# A non-local approximation of free discontinuity problems in SBV and SBD

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Let (M, g) be a complete Riemannian manifold with metric g and the Riemannian volume form dv. We consider the â„k-valued functions T âˆˆ [W-1,2(M) âˆ© LlocÂ¹(M)]k and u âˆˆ [W1,2(M)]k on M, where [W1,2(M)]k is a Sobolev space on M and [W-1,2(M)]k is its dual. We give a sufficient...