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

Open Mathematics

Murach Aleksandr¹  Los Valerii² 

[1] Institute of Mathematics, National Academy of Sciences of Ukraine, 3 Tereshchenkivs’ka, Kyiv, 01004, Ukraine;National Technical University of Ukraine Igor Sikorsky Kyiv Polytechnic Institute, Prospect Peremohy 37, 03056, Kyiv-56, Ukraine;

关键词: parabolic initial-boundary value problem;    hörmander space;    slowly varying function;    isomorphism property;    interpolation with a function parameter;    35k35;    46b70;    46e35;   

DOI  :  10.1515/math-2017-0008

来源: DOAJ

【 摘 要 】

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.

【 授权许可】

Unknown