On off-diagonal decay properties of the generalized Stokes semigroup with bounded measurable coefficients

2021/03/04 by Patrick Tolksdorf, Tolksdorf, Patrick
Computer Science · Mathematics · #Advanced Harmonic Analysis Research #Advanced Mathematical Modeling in Engineering #Advanced Mathematical Physics Problems #Analysis of PDEs (math.AP) #FOS: Mathematics #Functional Analysis (math.FA) #math.AP #math.FA

paper · pdf · doi:10.48550/arxiv.2103.03226

12 pages

arxiv created 2021/03/04 · openalex publication_date 2021/03/04 · arxiv updated 2021/03/05 · openalex created_date 2022/07/25 · openalex updated_date 2026/07/28

Abstract

We investigate off-diagonal decay properties of the generalized Stokes semigroup with bounded measurable coefficients on L²_σ (ℝ^d). Such estimates are well-known for elliptic equations in the form of pointwise heat kernel bounds and for elliptic systems in the form of integrated off-diagonal estimates. On our way to unveil this off-diagonal behavior we prove resolvent estimates in Morrey spaces L^{2 , ν} (ℝ^d) with 0 ≤ ν< 2.

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