Regularity of solutions to general parabolic problems in Hörmander spaces

TitleRegularity of solutions to general parabolic problems in Hörmander spaces
Publication TypeJournal Article
Year of Publication2017
AuthorsLos, VM, Mikhailets, VA, Murach, AA
Abbreviated Key TitleDopov. Nac. akad. nauk Ukr.
DOI10.15407/dopovidi2017.08.003
Issue8
SectionMathematics
Pagination3-10
Date Published8/2017
LanguageUkrainian
Abstract

We prove theorems on global and local regularities of generalized solutions to general parabolic initial-boundary-value problems in Hörmander spaces.
Keywordsgeneralized solution, Hörmander space, local regularity of a solution, parabolic initial-boundary-value problem
References: 
  1. Agranovich, M. S. & Vishik, M. I. (1964). Elliptic problems with parameters and parabolic problems of the general form. Usp. Mat. Nauk, 19, No. 3, pp. 53-161 (in Russian).
  2. Ladyzhenskaya, O. A., Solonnikov, V. A. & Ural'tseva, N. N. (1967). Linear and Quasilinear Equations of the Parabolic Type. Moscow: Nauka (in Russian).
  3. Lions, J.-L. & Magenes, E. (1972). Non-homogeneous boundary-value problems and applications. Vol. 2. Berlin: Springer.
  4. Zhitarashu, N. V. (1985). Theorems on complete collection of isomorphisms in the L2-theory of generaliz ed solutions for one equation parabolic in Petrovskii's sense. Mat. Sb., 128(170), No. 4, pp. 451-473 (in Russian).
  5. Ivasyshen, S. D. (1990). Green Matrices of Parabolic Boundary-Value Problems. Kiev: Vyshcha Shkola (in Russian).
  6. Eidel'man, S. D. (1994). Parabolic equations. In Partial differential equations, VI, Encyclopedia Mathe ma tics Sciences, Vol. 63 (pp. 205-316). Berlin: Springer.
  7. Eidel'man, S. D. & Zhitarashu, N. V. (1998). Parabolic boundary value problems. Basel: Birkhäuser. https://doi.org/10.1007/978-3-0348-8767-0
  8. Hörmander, L. (1963). Linear partial differential operators. Berlin: Springer. https://doi.org/10.1007/978-3-642-46175-0
  9. Mikhailets, V. A. & Murach, A. A. (2014). Hörmander spaces, interpolation, and elliptic problems. Berlin: De Gruyter. https://doi.org/10.1515/9783110296891
  10. Los, V. & Murach, A. A. (2013). Parabolic problems and interpolation with a function parameter. Methods Funct. Anal. Topology, 19, No. 2, pp. 146-160.
  11. 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
  12. Los, V. & Murach, A. (2017). Isomorphism theorems for some parabolic initial-boundary value problems in Hörmander spaces. Open Mathematics, 15, pp. 57-76. https://doi.org/10.1515/math-2017-0008
  13. 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). https://doi.org/10.15407/dopovidi2014.06.023
  14. Seneta, E. (1976). Regularly Varying Functions. Lecture Notes in Mathematics, vol. 508. Berlin: Springer. https://doi.org/10.1007/BFb0079658
  15. Los, V. M. (2016). Anisotropic Hörmander spaces on the lateral surface of a cylinder. J. Math. Sci., 217, No. 4, pp. 456-467. https://doi.org/10.1007/s10958-016-2985-9