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

Valerii Los, and Aleksandr Murach. "Isomorphism theorems for some parabolic initial-boundary value problems in Hörmander spaces." Open Mathematics 15.1 (2017): 57-76. <http://eudml.org/doc/288064>.

@article{ValeriiLos2017,
abstract = {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.},
author = {Valerii Los, Aleksandr Murach},
journal = {Open Mathematics},
keywords = {Parabolic initial-boundary value problem; Hörmander space; Slowly varying function; Isomorphism property; Interpolation with a function parameter; parabolic initial-boundary value problem; slowly varying function; isomorphism property; interpolation with a function parameter},
language = {eng},
number = {1},
pages = {57-76},
title = {Isomorphism theorems for some parabolic initial-boundary value problems in Hörmander spaces},
url = {http://eudml.org/doc/288064},
volume = {15},
year = {2017},
}

TY - JOUR
AU - Valerii Los
AU - Aleksandr Murach
TI - Isomorphism theorems for some parabolic initial-boundary value problems in Hörmander spaces
JO - Open Mathematics
PY - 2017
VL - 15
IS - 1
SP - 57
EP - 76
AB - 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.
LA - eng
KW - Parabolic initial-boundary value problem; Hörmander space; Slowly varying function; Isomorphism property; Interpolation with a function parameter; parabolic initial-boundary value problem; slowly varying function; isomorphism property; interpolation with a function parameter
UR - http://eudml.org/doc/288064
ER -