Parabolic boundary-value problems and generalized Sobolev spaces

Abstract

The research monograph expounds the foundation of a new theory of parabolic initial-boundary-value problems in scales of generalized anisotropic Sobolev spaces. These scales are calibrated essentially more finely with the help of a function parameter of regularity than the classes of spaces used earlier in the theory of parabolic problems. The monograph is featured by the systematic application of the method of quadratic interpolation (with function parameter) between abstract and Sobolev inner product spaces. The monograph is intended for the researches, professors, PhD students, and senior students specializing in differential equations and mathematical analysis.