Scholarlink

Abstract <p>The strong solvability of the Cauchy-Dirichlet problem for parabolic quasilinear equations with discontinuous data is investigated. The leading coefficients depend on the point (<i>x</i>, <i>t</i>) and on the solution <i>u</i>, the dependence on <i>x</i> is of the VMO type, while with respect to <i>t</i> only measurability is required from them. Under suitable structural conditions on the nonlinear terms, the existence and uniqueness of a strong solution is proved, which also turns out to be Hölder continuous.</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

A Quasilinear Cauchy-Dirichlet Problem for Parabolic Equations with VMOx Coefficients

  • 期刊论文

  • 发表日期：

    2025年3月1日

查看全文
  • R. Rescigno

摘要

Abstract

The strong solvability of the Cauchy-Dirichlet problem for parabolic quasilinear equations with discontinuous data is investigated. The leading coefficients depend on the point (x, t) and on the solution u, the dependence on x is of the VMO type, while with respect to t only measurability is required from them. Under suitable structural conditions on the nonlinear terms, the existence and uniqueness of a strong solution is proved, which also turns out to be Hölder continuous.