Analysis and boundary value problems on singular domains: an approach via bounded geometry
Analysis of PDEs
2019-04-15 v2 Mathematical Physics
Differential Geometry
math.MP
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.
Cite
@article{arxiv.1812.09898,
title = {Analysis and boundary value problems on singular domains: an approach via bounded geometry},
author = {Bernd Ammann and Nadine Grosse and Victor Nistor},
journal= {arXiv preprint arXiv:1812.09898},
year = {2019}
}
Comments
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