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<p>We consider degenerate parabolic Kolmogorov-type equations of any order with two groups of space variables of degeneration characterized, in addition, by the presence of degeneration in the initial hyperplane and the coefficients depending on all variables. For these equations, we construct the fundamental solution of the Cauchy problem and obtained estimates for this solution and its derivatives.</p>

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Fundamental Solution of the Cauchy Problem for Degenerate Parabolic Kolmogorov-Type Equations of Any Order with Degeneration on the Initial Hyperplane

  • 期刊论文

  • 发表日期：

    2026年5月25日

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  • O. H. Voznyak,
  • I. P. Medynskyi

摘要

We consider degenerate parabolic Kolmogorov-type equations of any order with two groups of space variables of degeneration characterized, in addition, by the presence of degeneration in the initial hyperplane and the coefficients depending on all variables. For these equations, we construct the fundamental solution of the Cauchy problem and obtained estimates for this solution and its derivatives.