Regular elliptic boundary-value problem in a two-sided refined scale of spaces

Details Regular elliptic boundary-value problem in a two-sided refined scale of spaces Regular elliptic boundary-value problem in a two-sided refined scale of spaces

2007-12-10

arxiv.org/abs/0712.1581v1

Ukrainian Math. J., 60 (2008), no. 4, 574 -- 597. (in English)

Mathematics

Analysis of PDEs

In Russian Abstract in English

Scientific paper

A regular elliptic boundary-value problem over a bounded domain with a smooth boundary is studied. We prove that the operator of this problem is a Fredholm one in the two-sided refined scale of the functional Hilbert spaces and generates a complete collection of isomorphisms. Elements of this scale are the isotropic spaces of Hormander-Volevich-Paneah and some its modifications. A priori estimate for the solution is established and its regularity is investigated.

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