Properties of integrals which have the type of derivatives of volume potentials for one ultraparabolic arbitrary order equation

Authors

  • V.S. Dron' Pidstryhach Institute for Applied Problems of Mechanics and Mathematics, 3b Naukova str., 79060, Lviv, Ukraine
  • S.D. Ivasyshen National Technical University of Ukraine ''Igor Sikorsky Kyiv Polytechnic Institute'', 7 Peremogy av., 03056, Kyiv, Ukraine https://orcid.org/0000-0001-5540-5345
  • I.P. Medyns'kyi Lviv Polytechnic National University, 12 Bandera str., 79013, Lviv, Ukraine https://orcid.org/0000-0002-0651-4198
https://doi.org/10.15330/cmp.11.2.268-280

Keywords:

ultraparabolic Kolmogorov type arbitrary order equation, an integral which have the type of derivatives of the volume potential, weight Hölder norm, Hölder space of increasing functions
Published online: 2019-12-31

Abstract

In weighted Hölder spaces it is studied the smoothness of integrals, which have the structure and properties of derivatives of volume potentials which generated by fundamental solutions of the Cauchy problem for one ultraparabolic arbitrary order equation of the Kolmogorov type. The coefficients in this equation depend only on the time variable. Special distances and norms are used for constructing of the weighted Hölder spaces.

The results of the paper can be used for establishing of the correct solvability of the Cauchy problem and estimates of solutions of the given non-homogeneous equation in corresponding weighted Hölder spaces.

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How to Cite
(1)
Dron', V.; Ivasyshen, S.; Medyns'kyi, I. Properties of Integrals Which Have the Type of Derivatives of Volume Potentials for One Ultraparabolic Arbitrary Order Equation. Carpathian Math. Publ. 2019, 11, 268-280.