Solvability of Gevrey boundary value problems for high order differential equation

Abstract

Singular integral operators of Gevrey problems for high-order parabolic equations with weighted conjugation (gluing) conditions are considered. In contrast to the classical case, the singular Cauchy operator together with the noncompact integral operators of a special form whose kernels are approximately homogeneous of degree −1 are among these operators. The Fredholm property criterion is established for these operators as well as formulas for their indexes. Examples of singular integral equations arising in the study of boundary value problems for forward- backward equations are displayed.