Sparse rectifiability and compactness in SBV
نویسندگان
چکیده
We introduce a notion of sparse rectifiability, stronger than that of uniform rectifiability. As applications we derive, firstly, results ensuring the convergence of the total variation measures |μ| subject to the weak* convergence of the sparsely rectifiable Radon measures μ. Secondly, we apply sparse rectifiability to derive compactness results for special functions of bounded variation (SBV) and, more generally, special functions of bounded deformation (SBD). Mathematics subject classification: 26B30, 28A33, 49J99.
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