Continuity results for degenerate diffusion equations with L^p_t L^q_x drifts

2019/06/12 by Sukjung Hwang, Yuming Paul Zhang, Hwang, Sukjung +1
Computer Science · Mathematics · #35B65 #35K55 #35K65 #Advanced Mathematical Modeling in Engineering #Analysis of PDEs (math.AP) #FOS: Mathematics #Mathematical Biology Tumor Growth #Nonlinear Partial Differential Equations

paper · pdf · doi:10.48550/arxiv.1906.04961

openalex publication_date 2019/06/12 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

In this paper, we study local uniform continuity of nonnegative weak solutions to degenerate diffusion-drift equations in the form u_t = Δu^m + ∇⋅ ( B (x,t) u), for m ≥ 1 assuming a vector field B ∈ L^p_t L^q_x. 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 continuity of B.

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