Boundary properties of solutions of differential equations and general boundary-value problems

Abstract

For a general differential operator with smooth matrix-valued coefficients in a bounded domain with smooth boundary we consider the boundary properties of functions from the domain of definition of a maximal extension in L 2 (Ω) and we study the properties of extensions and boundary-value problems corresponding to them. The investigations are based on Green's formula.

On weak solutions of boundary value problems for some general differential equations

“…Example 1. Some classes of differential operators satisfying (2.1) and (2.2) in a bounded domain were indicated in [13]. This list includes: i) scalar operators with constant coefficients, ii) scalar operators of principal type, iii) scalar operators of constant strength, iv) matrix operators with constant complex coefficients with the Paneah-Fuglede property, v) matrix operators which are uniformly elliptic in the sense of Douglis-Nirenberg in a domain with smooth b1oundary.…”