Scholarlink

Abstract <p> We consider the Cauchy problem for a spatially multidimensional second-order parabolicequation with Dini-continuous coefficients. The initial function belongs to the class of continuousand bounded functions with uniformly continuous and bounded first-order spatial derivatives. Theright-hand side of the equation can grow in a certain way when approaching the plane of theinitial data. The smoothness of the solution to this problem is investigated and estimates of thesolution and its first-order spatial derivatives are obtained using the Poisson potential and thevolume potential.</p>

错误：搜索内容不能为空，请输入英文关键词
错误：关键词超出字数限制，请精简
高级检索

On the Smoothness of the Solution to the Cauchy Problem for a Parabolic Equation with Dini-Continuous Coefficients

  • 期刊论文

  • 发表日期：

    2025年10月1日

查看全文
  • I. V. Zhenyakova,
  • M. F. Cherepova

摘要

Abstract

We consider the Cauchy problem for a spatially multidimensional second-order parabolicequation with Dini-continuous coefficients. The initial function belongs to the class of continuousand bounded functions with uniformly continuous and bounded first-order spatial derivatives. Theright-hand side of the equation can grow in a certain way when approaching the plane of theinitial data. The smoothness of the solution to this problem is investigated and estimates of thesolution and its first-order spatial derivatives are obtained using the Poisson potential and thevolume potential.