Analysis and boundary value problems on singular domains: an approach via bounded geometry

2018/12/24 by Bernd Ammann, Nadine Grosse, Nadine Große +4
Computer Science · Mathematics · Physics and Astronomy · #Advanced Mathematical Modeling in Engineering #Analysis of PDEs (math.AP) #Differential Equations and Boundary Problems #Differential Geometry (math.DG) #FOS: Mathematics #FOS: Physical sciences #Mathematical Physics (math-ph) #Numerical methods in inverse problems #Spectral Theory in Mathematical Physics #math-ph #math.AP #math.DG #math.MP

paper · pdf · doi:10.48550/arxiv.1812.09898

8 pages, announcement with sketches of the proofs and a summary in French. v2: title slightly changed, small changes in the text, final version. To appeat in Comptes Rendus Mathematique

openalex publication_date 2018/12/24 · arxiv created 2019/04/12 · arxiv updated 2019/04/15 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We prove well-posedness and regularity results for elliptic boundary value problems on certain domains with a smooth set of singular points. Our class of domains contains the class of domains with isolated oscillating conical singularities, and hence they generalize the classical results of Kondratiev on domains with conical singularities. The proofs are based on conformal changes of metric, on the differential geometry of manifolds with boundary and bounded geometry, and on our earlier results on manifolds with boundary and bounded geometry.

Related

• Differential operators on domains with conical points: precise uniform regularity estimates
• Boundary behavior for a singular quasi-linear elliptic equation
• First-order elliptic boundary value problems on manifolds with non-compact boundary
• Some elliptic problems with singular nonlinearity and advection for Riemannian manifolds
• Boundary Behaviors for Liouville's Equation in Planar Singular Domains