Scholarlink

<p>We use the framework of the first-order differential structure in metric measure spaces introduced by Gigli to define a notion of weak solution to gradient flows of convex, lower semicontinuous and coercive functionals. We prove their existence and uniqueness and show that they are also variational solutions; in particular, this is an existence result for variational solutions. Then, we apply this technique in the case of a gradient flow of a functional with inhomogeneous growth.</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

Weak solutions to gradient flows of functionals with inhomogeneous growth in metric spaces

  • 期刊论文

  • 出版模式：

    开放获取

  • 发表日期：

    2025年5月4日

查看全文
  • Wojciech Górny

摘要

We use the framework of the first-order differential structure in metric measure spaces introduced by Gigli to define a notion of weak solution to gradient flows of convex, lower semicontinuous and coercive functionals. We prove their existence and uniqueness and show that they are also variational solutions; in particular, this is an existence result for variational solutions. Then, we apply this technique in the case of a gradient flow of a functional with inhomogeneous growth.