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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...

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