Fractional Sobolev norms and BV functions on manifolds
classification
🧮 math.FA
math.APmath.MG
keywords
sobolevfunctionsmanifoldsboundedcompactfractionalseminormvariation
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The bounded variation seminorm and the Sobolev seminorm on compact manifolds are represented as a limit of fractional Sobolev seminorms. This establishes a characterization of functions of bounded variation and of Sobolev functions on compact manifolds. As an application the special case of sets of finite perimeter is considered.
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