Neumann problem for p-Laplace equation in metric spaces using a\n variational approach: existence, boundedness, and boundary regularity

2016/09/21 by Lukáš Malý, Malý, Lukáš, Nageswari Shanmugalingam +1 · 1 citation
Computer Science · Mathematics · #30E25 #30L99 #31E05 (Primary) #46E35 (Secondary) #Advanced Mathematical Modeling in Engineering #Analysis of PDEs (math.AP) #FOS: Mathematics #Geometric Analysis and Curvature Flows #Metric Geometry (math.MG) #Nonlinear Partial Differential Equations

paper · pdf · doi:10.48550/arxiv.1609.06808

openalex publication_date 2016/09/21 · openalex created_date 2022/10/01 · openalex updated_date 2026/07/28

Abstract

We employ a variational approach to study the Neumann boundary value problem\nfor the p-Laplacian on bounded smooth-enough domains in the metric setting,\nand show that solutions exist and are bounded. The boundary data considered are\nBorel measurable bounded functions. We also study boundary continuity\nproperties of the solutions. One of the key tools utilized is the trace theorem\nfor Newton-Sobolev functions, and another is an analog of the De Giorgi\ninequality adapted to the Neumann problem.\n

Citations

• Fine continuity on metric spaces
• Metric measure spaces with Riemannian Ricci curvature bounded from below
• Quasiconformal maps in metric spaces with controlled geometry
• Trace and extension theorems for Sobolev-type functions in metric spaces

Cited by

• Regularity for quasilinear elliptic equations in metric measure spaces

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