Boundary Regularity for the ∞-Heat Equation

2017/09/27 by Nikolai Ubostad, Ubostad, Nikolai
Computer Science · Engineering · Mathematics · #Advanced Mathematical Modeling in Engineering #Analysis of PDEs (math.AP) #FOS: Mathematics #Nonlinear Partial Differential Equations #Stability and Controllability of Differential Equations

paper · pdf · doi:10.48550/arxiv.1709.09487

openalex publication_date 2017/09/27 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We study the boundary regularity for the normalised ∞-heat equation u_t = Δ_∞^Nu in arbitrary domains. Perron's Method is used for constructing solutions. We characterize regular boundary points with barrier functions, and prove an Exterior Ball result. A Petrovsky-like criterion is established.

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