2b-anisotropic Hörmander spaces in cylindrical domains

Title2b-anisotropic Hörmander spaces in cylindrical domains
Publication TypeJournal Article
Year of Publication2018
AuthorsLos, VM
Abbreviated Key TitleDopov. Nac. akad. nauk Ukr.
DOI10.15407/dopovidi2018.06.003
Issue6
SectionMathematics
Pagination3-8
Date Published6/2018
LanguageUkrainian
Abstract

We introduce a class of 2b-anisotropic inner product Hörmander spaces in a cylindrical domain. These spaces are obtained by the interpolation with a function parameter between anisotropic Sobolev spaces. A new condition for the continuity of distributions from the introduced spaces together with generalized partial derivatives up to some order is obtained.
Keywords2b-anisotropic Hörmander space, cylindrical domain, interpolation with a function parameter
References: 
  1. Hörmander, L. (1963). Linear partial differential operators. Berlin: Springer. doi: https://doi.org/10.1007/978-3-642-46175-0
  2. Mikhailets, V. A. & Murach, A. A. (2014). Hörmander spaces, interpolation, and elliptic problems. Berlin: De Gruyter. doi: https://doi.org/10.1515/9783110296891
  3. Los, V. & Murach, A. A. (2013). Parabolic problems and interpolation with a function parameter. Methods Funct. Anal. Topol., 19, No. 2, pp. 146-160.
  4. Los, V. M. (2015). Mixed problems for the two-dimensional heat-conduction equation in anisotropic Hörmander spaces. Ukr. Math. J., 67, No. 5, pp. 735-747. doi: https://doi.org/10.1007/s11253-015-1111-3
  5. Los, V., Mikhailets, V. A. & Murach, A. A. (2017). An isomorphism theorem for parabolic problems in Hörmander spaces and its applications. Commun. Pur. Appl. Anal., 16, No. 1. pp. 69-97. doi: https:// doi.org/10.3934/cpaa.2017003
  6. Los, V. & Murach, A. (2017). Isomorphism theorems for some parabolic initial-boundary value problems in Hörmander spaces. Open Mathematics, 15, pp. 57-76. doi: https://doi.org/10.1515/math-2017-0008
  7. Los, V. M. & Murach, A. A. (2014). Parabolic mixed problems in spaces of generalized smoothness. Dopov. Nac. akad. nauk. Ukr., No. 6, pp. 23-31 (in Russian). doi: https://doi.org/10.15407/dopovidi2014.06.023
  8. Los, V. M. (2016). Anisotropic Hörmander spaces on the lateral surface of a cylinder. J. Math. Sci., 217, No. 4. pp. 456-467. doi: https://doi.org/10.1007/s10958-016-2985-9
  9. Volevich, L. R. & Paneah, B. P. (1965). Certain spaces of generalized functions and embedding theorems. Russ. Math. Surv., 20, No. 1. pp. 1-73. doi: https://doi.org/10.1070/RM1965v020n01ABEH004139
  10. Seneta, E. (1976). Regularly varying functions. Lecture notes in mathematics, vol. 508. Berlin: Springer. doi: https://doi.org/10.1007/BFb0079658
  11. Mikhailets, V. A. & Murach, A. A. (2008). Interpolation with a function parameter and refined scale of spaces. Methods Funct. Anal. Topol., 14, No. 1, pp. 81-100.