On the structure of diffuse measures for parabolic capacities
| Autor: | Andrzej Rozkosz, Tomasz Klimsiak |
|---|---|
| Rok vydání: | 2018 |
| Předmět: |
010102 general mathematics
Zero (complex analysis) Structure (category theory) General Medicine 01 natural sciences Combinatorics Mathematics - Analysis of PDEs Bounded function 0103 physical sciences Radon measure Converse FOS: Mathematics 010307 mathematical physics 0101 mathematics Mathematics Analysis of PDEs (math.AP) |
| DOI: | 10.48550/arxiv.1808.06422 |
| Popis: | Let Q = ( 0 , T ) × Ω , where Ω is a bounded open subset of R d . We consider the parabolic p-capacity on Q naturally associated with the usual p-Laplacian. Droniou, Porretta, and Prignet have shown that if a bounded Radon measure μ on Q is diffuse, i.e. charges no set of zero p-capacity, p > 1 , then it is of the form μ = f + div ( G ) + g t for some f ∈ L 1 ( Q ) , G ∈ ( L p ′ ( Q ) ) d and g ∈ L p ( 0 , T ; W 0 1 , p ( Ω ) ∩ L 2 ( Ω ) ) . We show the converse of this result: if p > 1 , then each bounded Radon measure μ on Q admitting such a decomposition is diffuse. |
| Databáze: | OpenAIRE |
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