Abstract A theorem about the behavior of Cauchy-type integrals at the endpoints of the integration contour and at discontinuity points of the density is stated, and its application to boundary value problems for 2 n- order parabolic equations with a changing direction of time are described. The theory of singular equations, along with the smoothness of the initial data, makes it possible to specify necessary and sufficient conditions for the solution to belong to Hölder spaces. Note that, in the case n = 3, the smoothness of the initial data and the solvability conditions imply that the solution belongs to smoother spaces near the ends with respect to the time variable.

中文翻译：

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随时间变化的抛物线方程

摘要 阐述了关于柯西型积分在积分轮廓端点和密度不连续点处的行为的定理，并描述了它在时间方向变化的 2 n 阶抛物线方程边值问题中的应用。 . 奇异方程理论以及初始数据的平滑性使得可以指定解属于 Hölder 空间的充分必要条件。请注意，在 n = 3 的情况下，初始数据的平滑度和可解性条件意味着解属于相对于时间变量靠近端点的更平滑空间。