Rough traces of $BV$ functions in metric measure spaces
| Autor: | Michele Miranda, Vito Buffa |
|---|---|
| Rok vydání: | 2019 |
| Předmět: |
metric measure spaces
Pure mathematics Trace (linear algebra) Poincaré inequality Context (language use) Lebesgue integration Measure (mathematics) NO symbols.namesake Mathematics - Analysis of PDEs Mathematics - Metric Geometry FOS: Mathematics PE1_8 Integration by parts Functions of bounded variation Mathematics Metric Geometry (math.MG) 26A45 (Primary) 26B20 30L99 46E35 (Secondary) Articles traces Functions of bounded variation metric measure spaces traces integration by parts formulas Functional Analysis (math.FA) Mathematics - Functional Analysis Metric (mathematics) Bounded variation symbols integration by parts formulas Analysis of PDEs (math.AP) |
| Zdroj: | Annales Fennici Mathematici |
| DOI: | 10.48550/arxiv.1907.01673 |
| Popis: | Following a Maz'ya-type approach, we adapt the theory of rough traces of functions of bounded variation ($BV$) in the context of doubling metric measure spaces supporting a Poincar\'e inequality. This eventually allows for an integration by parts formula involving the rough trace of such a function. We then compare our analysis with the discussion done in a recent work by P. Lahti and N. Shanmugalingam, where traces of $BV$ functions are studied by means of the more classical Lebesgue-point characterization, and we determine the conditions under which the two notions coincide. |
| Databáze: | OpenAIRE |
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