On dimKer and dimCoker for an Elliptic Operator with Discontinuous Coefficients

Abstract

For divergence form of elliptic operator with discontinuous piecewise smooth coefficients we analyzed questions of the uniqueness and the existence of generalized solutions for BVP with the divergent right-hand part from the class with first derivatives from in a bounded plain domains with smooth and nonsmooth borders. We calculate dimKer and dimCoker for an elliptic operator for all indices depending on parameters of critical points.