Analysis and boundary value problems on domains with a smooth set of singular points: an approach via bounded geometry
by
Bernd Ammann, Nadine Große, Victor Nistor


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Abstract

We prove well-posedness and regularity results for elliptic boundary value problems on certain singular domains. Our class of domains contains the class of domains with isolated oscillating conical singularities. Our results thus 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.

Mathematics Subject Classification

38J40 (Primary), 47L80, 58H05, 46L87, 46L80 (Secondary)
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The Paper was written on 1.3.2019
Last update 1.3.2019