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

V. Dron' | Zendy; S. D. Іvasyshen | Zendy; I. P. Medynskyi | Zendy

Open Access

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

Author(s) -

V. Dron',

S. D. Іvasyshen,

I. P. Medynskyi

Publication year - 2019

Publication title -

carpathian mathematical publications

Language(s) - English

Resource type - Journals

SCImago Journal Rank - 0.63

H-Index - 4

eISSN - 2313-0210

pISSN - 2075-9827

DOI - 10.15330/cmp.11.2.268-280

Subject(s) - mathematics , smoothness , type (biology) , homogeneous , cauchy distribution , order (exchange) , initial value problem , mathematical analysis , cauchy problem , variable (mathematics) , pure mathematics , volume (thermodynamics) , combinatorics , ecology , finance , economics , biology , physics , quantum mechanics

In weighted Holder 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 Holder 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 Holder spaces.

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