Extension theorems for external cusps with minimal regularity

Sobolev functions defined on certain simple domains with an isolated sin- gular point (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 de- veloped for dealing with uniform domains. The weight involved in the ex- tension appears as a consequence of the failure of the domain to comply with basic properties of 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 that are given by a monotonic function either of the distance to the boundary or of the distance to the tip of the cusp. Fil: Acosta Rodriguez, Gabriel. Consejo Nacional de Investigaciones Científicas y Técnicas. Oficina de Coordinación Administrativa Ciudad Universitaria. Instituto de Investigaciones Matemáticas "Luis A. Santaló". Universidad de Buenos Aires. Facultad de Ciencias Exactas y Naturales. Instituto de Investigaciones Matemáticas "Luis A. Santaló"; Argentina Fil: Ojea, Ignacio. Consejo Nacional de Investigaciones Científicas y Técnicas. Oficina de Coordinación Administrativa Ciudad Universitaria. Instituto de Investigaciones Matemáticas "Luis A. Santaló". Universidad de Buenos Aires. Facultad de Ciencias Exactas y Naturales. Instituto de Investigaciones Matemáticas "Luis A. Santaló"; Argentina