CONICET | Buscador de Institutos y Recursos Humanos

Sobolev functions defined on very simple domains with an isolated singularpoint (such as power type external cusps) can not be extended in standard but in appropriate weighted spaces. In this article we show that this result holds for a large class of domains that generalizes external cusps, allowing minimal boundary regularity. The construction of our extension operator is based on a modification of reflection techniques originally developed for dealing with uniform domains. The weight involved in the extension appears as a consequence of the failure of the domain to comply with basic properties of locally uniform domains, and it turns out to be a quantification of that failure. We show that weighted, rather than standard spaces, can be treated with our approach for weights which are given by a monotonic function either of the distance to the boundary or of the distance to the tip of the cusp.