Isomorphism theorems for some parabolic initial-boundary value problems in Hörmander spaces

• Autorzy: Valerii Los , Aleksandr Murach
• Języki publikacji: EN

Abstrakty

EN

In Hörmander inner product spaces, we investigate initial-boundary value problems for an arbitrary second order parabolic partial differential equation and the Dirichlet or a general first-order boundary conditions. We prove that the operators corresponding to these problems are isomorphisms between appropriate Hörmander spaces. The regularity of the functions which form these spaces is characterized by a pair of number parameters and a function parameter varying regularly at infinity in the sense of Karamata. Owing to this function parameter, the Hörmander spaces describe the regularity of functions more finely than the anisotropic Sobolev spaces.

Słowa kluczowe

EN

Parabolic initial-boundary value problem; Hörmander space; Slowly varying function; Isomorphism property; Interpolation with a function parameter

Kategorie tematyczne

• 35K35: Initial-boundary value problems for higher-order parabolic equations
• 46B70: Interpolation between normed linear spaces
• 46E35: Sobolev spaces and other spaces of ``smooth'' functions, embedding theorems, trace theorems

• Wydawca: De Gruyter Open
• Czasopismo: Open Mathematics
• Rocznik: 2017
• Tom: 15
• Numer: 1
• Strony: 57-76

Daty

wydano

2017-01-01

otrzymano

2016-11-29

zaakceptowano

2017-01-16

online

2017-02-15

Twórcy

autor

Valerii Los

• National Technical University of Ukraine Igor Sikorsky Kyiv Polytechnic Institute, Prospect Peremohy 37, 03056, Kyiv-56,

autor

Aleksandr Murach

• Institute of Mathematics, National Academy of Sciences of Ukraine, 3 Tereshchenkivs’ka, Kyiv, 01004, Ukraine and Chernihiv National Pedagogical University Het’mana Polubotka str. 53, 14013 Chernihiv,

Identyfikatory

DOI

10.1515/math-2017-0008