Scholarlink

<p>In this paper, we introduce weak optimal entropy transport problems that cover both optimal entropy transport problems and weak optimal transport problems introduced by Liero et al. (Invent. Math. <b>211</b>(3), 969–1117, <CitationRef CitationID="CR27">2018</CitationRef>) and Gozlan et al. (J. Funct. Anal. <b>273</b>(11), 3327–3405, <CitationRef CitationID="CR20">2017</CitationRef>), respectively. Under some mild assumptions of entropy functionals, we establish a Kantorovich type duality for our weak optimal entropy transport problem. As consequences, via a different method, we recover both Kantorovich duality formulas for optimal entropy transport problems (Liero et al., Invent. Math. <b>211</b>(3), 969–1117, <CitationRef CitationID="CR27">2018</CitationRef>), and weak optimal transport problems (Backhoff-Veraguas et al., Calc. Var. Partial Differential Equations <b>58</b>(6), 203, <CitationRef CitationID="CR5">2019</CitationRef>; Gozlan et al., J. Funct. Anal. <b>273</b>(11), 3327–3405, <CitationRef CitationID="CR20">2017</CitationRef>).</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 Optimal Entropy Transport Problems

  • 期刊论文

  • 发表日期：

    2025年5月29日

查看全文
  • Nhan-Phu Chung,
  • Thanh-Son Trinh

摘要

In this paper, we introduce weak optimal entropy transport problems that cover both optimal entropy transport problems and weak optimal transport problems introduced by Liero et al. (Invent. Math. 211(3), 969–1117, 2018) and Gozlan et al. (J. Funct. Anal. 273(11), 3327–3405, 2017), respectively. Under some mild assumptions of entropy functionals, we establish a Kantorovich type duality for our weak optimal entropy transport problem. As consequences, via a different method, we recover both Kantorovich duality formulas for optimal entropy transport problems (Liero et al., Invent. Math. 211(3), 969–1117, 2018), and weak optimal transport problems (Backhoff-Veraguas et al., Calc. Var. Partial Differential Equations 58(6), 203, 2019; Gozlan et al., J. Funct. Anal. 273(11), 3327–3405, 2017).