Integral inequalities for functions with zero traces on \(C^ 0\)-manifolds and their applications. (Q1432537)

From the introducton: We prove some integral inequalities of the type of embedding theorems for functions from the Sobolev weight classes with zero traces on \(C^0\)-manifolds of dimension \(m\) in the Euclidean space \(R_n\), where \(m<n\). A manifold of dimension zero is, by definition, a set of finitely many points. Of special interest is the case of a manifold with boundary. Integral inequalities of this type are used to analyze degenerating elliptic equations in the theory of boundary value problems, to study the closure of the set of compactly supported infinitely differentiable functions in weighted functional spaces, and to examine spectral asymptotic behaviors of differential operators.