H\"ormander Spaces, Interpolation, and Elliptic Problems

TL;DR

This monograph systematically develops the theory of elliptic operators and boundary-value problems within H"ormander spaces, utilizing interpolation methods with functional parameters, and introduces new results even for Sobolev scales.

Contribution

It provides the first comprehensive exposition of elliptic problems in H"ormander spaces using interpolation with a functional parameter, including novel results for Sobolev scales.

Findings

Systematic theory of elliptic operators in H"ormander spaces

Interpolation with a functional parameter as a key method

New results for Sobolev scales

Abstract

The research monograph gives the first systematic exposition of the elliptic (scalar and matrix) operators theory and elliptic boundary-value problems in the scales of Hilbert spaces of H\"ormander of the functions/distributions of arbitrary positive or negative smoothness. The book is based on the method of interpolation with a functional parameter for the abstract and Sobolev unitary spaces. Some results are also new for the Sobolev scales. The monograph is intended for the researches, professors and PhD students.