University of Massachusetts Amherst
	Department of Mathematics and Statistics
	Applied Mathematics and Computation Seminar

Abstract: It is well know that differential equations and corresponding boundary value problems generate natural spaces where the problem should be considered. In this context Sobolev spaces and their properties (embedding, compactness, traces and etc. results) play an important role. However, if the equations have coefficients with degenerations or singularities Sobolev type spaces with weights are more suitable for them. Moreover, if weights have weak degenerations on the boundary of the domain the functions from weighted Sobolev spaces have traces. However, for strongly degenerated weights the functions from the corresponding Sobolev type spaces may have no boundary values in classic sense. In this talk we are going to discuss our vision of boundary values for functions from such type of spaces. We introduce the notion of a weighted boundary value and discuss its properties. Also, we consider an application of our results to one class of boundary value problems.