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

## TL;DR

This paper establishes well-posedness and regularity for elliptic boundary value problems on domains with singular points, extending classical results to more complex geometries using geometric and conformal techniques.

## Contribution

It introduces a new approach to analyze elliptic problems on singular domains via bounded geometry and conformal metric changes, broadening the scope of classical conical singularity results.

## Key findings

- Proves well-posedness of elliptic boundary value problems on singular domains.
- Establishes regularity results for solutions in these domains.
- Generalizes Kondratiev's classical results to domains with oscillating conical singularities.

## 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.