Regularity and Capacity for the Fractional Dissipative Operator

2012/12/04 by Renjin Jiang, Jiang, Renjin, Jie Xiao +5
Computer Science · Mathematics · #31C15 (Primary) #35K05 #Advanced Harmonic Analysis Research #Advanced Mathematical Modeling in Engineering #Analysis of PDEs (math.AP) #FOS: Mathematics #Functional Analysis (math.FA) #Nonlinear Partial Differential Equations

paper · pdf · doi:10.48550/arxiv.1212.0744

openalex publication_date 2012/12/04 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

This note is devoted to exploring some analytic-geometric properties of the regularity and capacity associated to the so-called fractional dissipative operator ∂_t+(-Δ)^α, naturally establishing a diagonally sharp Hausdorff dimension estimate for the blow-up set of a weak solution to the fractional dissipative equation (∂_t+(-Δ)^α)u(t,x)=F(t,x) subject to u(0,x)=0.

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