Parabolic problems and interpolation with a function parameter

Authors

  • A. A. Murach Department of Higher and Applied Mathematics, Chernigiv State Technological University, 95 Shevchenka, Chernigiv, 14027, Ukraine
  • V. N. Los Institute of Mathematics, National Academy of Sciences of Ukraine, 3 Tereshchenkivs'ka, Kyiv, 01601, Ukraine

DOI:

Keywords:

Parabolic problem, interpolation with a function parameter, anisotropic Sobolev space, space of generalized smoothness, refined Sobolev scale, slowly varying function, isomorphism property

Abstract

We give an application of interpolation with a function parameter to parabolic differential operators. We introduce a 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 initial--boundary 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.

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Published

2013-06-25

Issue

Vol. 19 No. 2 (2013)

Section

Articles

How to Cite

Murach, A. A., and V. N. Los. “Parabolic Problems and Interpolation With a Function Parameter”. Methods of Functional Analysis and Topology, vol. 19, no. 2, June 2013, pp. 146-60, https://zen.imath.kiev.ua/index.php/mfat/article/view/542.