Oblique Derivative Boundary Value Problems on Families of Planar Domains

2021/08/23 by Ziming Shi, Shi, Ziming
Computer Science · Mathematics · #30E25 #30G20 #35J25 #45E05 #Advanced Mathematical Modeling in Engineering #Algebraic and Geometric Analysis #Analysis of PDEs (math.AP) #Complex Variables (math.CV) #Differential Equations and Boundary Problems #FOS: Mathematics

paper · pdf · doi:10.48550/arxiv.2108.10287

openalex publication_date 2021/08/23 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We consider second-order elliptic equations with oblique derivative boundary conditions, defined on a family of bounded domains in ℂ that depend smoothly on a real parameter λ∈ [0,1]. We derive sharp regularity properties of the solutions in all variables, including the parameter λ. More specifically we show that the solution and its derivatives are continuous in all variables, and the Hölder norms of the space variables are bounded uniformly in λ.

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