Boundary regularity for a degenerate elliptic equation with mixed\n boundary conditions

2018/03/28 by Alassane Niang, Niang, Alassane
Computer Science · Mathematics · #35J70 (35J47) #Advanced Mathematical Modeling in Engineering #Analysis of PDEs (math.AP) #FOS: Mathematics #Nonlinear Partial Differential Equations #Numerical methods in inverse problems

paper · pdf · doi:10.48550/arxiv.1803.10641

openalex publication_date 2018/03/28 · openalex created_date 2022/10/07 · openalex updated_date 2026/07/28

Abstract

We consider a function U satisfying a degenerate elliptic equation on\n(0,+\∞)\× R^N with mixed Dirichlet-Neumann boundary conditions. The\nNeumann condition is prescribed on a bounded domain \Ω\⊂ R^N of class\nC^1;1, whereas the Dirichlet data is on the exterior of \Ω. We prove\nHolder regularity estimates of U/d^s, where d is a distance function defined\nas d(z) := dist(z;R^N\∖\Ω), for z\∈ (0,+\∞)\× R^N. The\ndegenerate elliptic equation arises from the Caffarelli-Silvestre extension of\nthe Dirichlet problem for the fractional Laplacian. Our proof relies on\ncompactness and blow-up analysis arguments.\n

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