Parabolic problems and interpolation with a function parameter
Abstract
We give an application of interpolation with a function parameter to parabolic differential operators. We introduce the refined anisotropic Sobolev scale that consists of some Hilbert function spaces of generalized smoothness. The latter is characterized by a real number and a function varying slowly at infinity in Karamata's sense. This scale is connected with anisotropic Sobolev spaces by means of interpolation with a function parameter. We investigate a general initialboundary value parabolic problem in the refined Sobolev scale. We prove that the operator corresponding to this problem sets isomorphisms between appropriate spaces pertaining to this scale.
 Publication:

arXiv eprints
 Pub Date:
 April 2013
 DOI:
 10.48550/arXiv.1304.2552
 arXiv:
 arXiv:1304.2552
 Bibcode:
 2013arXiv1304.2552L
 Keywords:

 Mathematics  Analysis of PDEs;
 Mathematics  Functional Analysis;
 Primary 35K35;
 46B70;
 Secondary 46E35
 EPrint:
 18 pages