Generalized Potentials and Boundary Equations with Projections for Differential Operators

Abstract

In this chapter we introduce the notion of a clear trace and define surface potentials with density from the space of clear traces. For differential equations in a domain, we construct equivalent equations on the boundary of this domain, which must be solved for the unknown density from the space of clear traces. These boundary equations contain a projection in their structure. They are a generalization of the classical Sokhotskii-Plemelj conditions in the theory of analytic functions (of the Cauchy-Riemann equations) and of the Calderon-Seeley boundary equations [109, 110].