Scholarlink

Abstract <p>The character of the regularity of the Poisson potential for a uniformly parabolic equation with Dini-continuous coefficients is studied. The potential density is continuous and bounded with all derivatives up to and including the second order. In particular, it follows from the results that the Dini condition for the principal coefficients of the equation is sharp for the existence of a regular solution to the Cauchy problem in the form of a Poisson 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

The Poisson Potential 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
  • E. A. Baderko,
  • K. V. Semenov

摘要

Abstract

The character of the regularity of the Poisson potential for a uniformly parabolic equation with Dini-continuous coefficients is studied. The potential density is continuous and bounded with all derivatives up to and including the second order. In particular, it follows from the results that the Dini condition for the principal coefficients of the equation is sharp for the existence of a regular solution to the Cauchy problem in the form of a Poisson potential.