Continuity results for degenerate diffusion equations with LtpLxq drifts. (October 2021)

• Record Type: Journal Article
• Authors: Hwang, Sukjung; Zhang, Yuming Paul
• Is Part Of: Nonlinear analysis. Volume 211(2021)
• Publication Date: 2021-10
• Subjects: 35B65 -- 35K55 -- 35K65; Degenerate diffusion -- Drift equations -- Uniform continuity -- Hölder continuity -- Critical bounds; Mathematical analysis -- Periodicals; Functional analysis -- Periodicals; Nonlinear theories -- Periodicals; Analyse mathématique -- Périodiques; Analyse fonctionnelle -- Périodiques; Théories non linéaires -- Périodiques; Functional analysis; Mathematical analysis; Nonlinear theories; Periodicals; Electronic journals; 515.7248
• DOI: 10.1016/j.na.2021.112413
• Languages: English
• ISSNs: 0362-546X

Abstract

Abstract: In this paper, we study local uniform continuity of nonnegative weak solutions to degenerate diffusion-drift equations in the form of u t = Δ u m + ∇ ⋅ B ( x, t ) u, for m ≥ 1 assuming a vector field B ∈ L t p L x q . Regarding local Hölder continuity, we provide a sharp condition on p and q, which is referred to as the subcritical region. In the critical region, the divergence-free condition is essential to providing uniform continuity which depends on the modulus of continuity of the local norm of B .