Global gradient estimates for a general type of nonlinear parabolic equations

2020/05/30 by Cecilia Cavaterra, Cavaterra, Cecilia, Serena Dipierro +5
Mathematics · #Analysis of PDEs (math.AP) #FOS: Mathematics #Geometric Analysis and Curvature Flows #Navier-Stokes equation solutions #Nonlinear Partial Differential Equations

paper · pdf · doi:10.48550/arxiv.2006.00263

openalex publication_date 2020/05/30 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We provide global gradient estimates for solutions to a general type of nonlinear parabolic equations, possibly in a Riemannian geometry setting. Our result is new in comparison with the existing ones in the literature, in light of the validity of the estimates in the global domain, and it detects several additional regularity effects due to special parabolic data. Moreover, our result comprises a large number of nonlinear sources treated by a unified approach, and it recovers many classical results as special cases.

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