General parabolic initial-boundary value problems in H\"ormander spaces

TL;DR

This paper studies a broad class of parabolic initial-boundary value problems within anisotropic H"ormander spaces, proving isomorphism of operators and demonstrating local regularity improvements of solutions.

Contribution

It establishes the isomorphism of operators in anisotropic H"ormander spaces and proves local regularity enhancement for solutions to these parabolic problems.

Findings

Operators are isomorphisms between H"ormander spaces.

Solutions exhibit local increase in regularity.

Framework applies to general nonhomogeneous parabolic problems.

Abstract

We investigate a general nonhomogeneous parabolic initial-boundary value problem in some anisotropic H\"ormander inner product spaces. We prove that the operators corresponding to this problem are isomorphisms between appropriate H\"ormander spaces. As an application of this result, we establish a theorem on the local increase in regularity of solutions to the problem.