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

Valerii Los;  Aleksandr Murach — 2017

Open Mathematics

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...

Elliptic Systems of Pseudodifferential Equations in the Refined Scale on a Closed Manifold

Vladimir A. Mikhailets;  Aleksandr A. Murach — 2008

Bulletin of the Polish Academy of Sciences. Mathematics

We study a system of pseudodifferential equations which is elliptic in the Petrovskii sense on a closed smooth manifold. We prove that the operator generated by the system is a Fredholm operator in a refined two-sided scale of Hilbert function spaces. Elements of this scale are special isotropic spaces of Hörmander-Volevich-Paneah.

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