Besov class via heat semigroup on Dirichlet spaces III: BV functions and sub-Gaussian heat kernel estimates
| Autor: | Patricia Alonso-Ruiz, Fabrice Baudoin, Li Chen, Luke Rogers, Nageswari Shanmugalingam, Alexander Teplyaev |
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| Rok vydání: | 2021 |
| Předmět: |
Applied Mathematics
Probability (math.PR) 010102 general mathematics FOS: Physical sciences Metric Geometry (math.MG) Mathematical Physics (math-ph) 16. Peace & justice 01 natural sciences Functional Analysis (math.FA) Mathematics - Functional Analysis 010104 statistics & probability Mathematics - Analysis of PDEs Mathematics - Metric Geometry FOS: Mathematics Mathematics::Metric Geometry 0101 mathematics Mathematical Physics Mathematics - Probability Analysis Analysis of PDEs (math.AP) |
| Zdroj: | Calculus of Variations and Partial Differential Equations. 60 |
| ISSN: | 1432-0835 0944-2669 |
| Popis: | With a view toward fractal spaces, by using a Korevaar-Schoen space approach, we introduce the class of bounded variation (BV) functions in a general framework of strongly local Dirichlet spaces with a heat kernel satisfying sub-Gaussian estimates. Under a weak Bakry-\'Emery curvature type condition, which is new in this setting, this BV class is identified with a heat semigroup based Besov class. As a consequence of this identification, properties of BV functions and associated BV measures are studied in detail. In particular, we prove co-area formulas, global $L^1$ Sobolev embeddings and isoperimetric inequalities. It is shown that for nested fractals or their direct products the BV class we define is dense in $L^1$. The examples of the unbounded Vicsek set, unbounded Sierpinski gasket and unbounded Sierpinski carpet are discussed. Comment: The notes arXiv:1806.03428 will be divided in a series of papers. This is the third paper. v2: Final version v3: The proof of Theorem 3.9 contained an error which is corrected in this version |
| Databáze: | OpenAIRE |
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