Hölder continuity and bounds for fundamental solutions to nondivergence form parabolic equations

Seiichiro Kusuoka

研究成果: Article査読

8 被引用数 (Scopus)

抄録

We consider nondegenerate second-order parabolic partial differential equations in nondivergence form with bounded measurable coefficients (not necessary continuous). Under certain assumptions weaker than the Hölder continuity of the coefficients, we obtain Gaussian bounds and Hölder continuity of the fundamental solution with respect to the initial point. Our proofs employ pinned diffusion processes for the probabilistic representation of fundamental solutions and the coupling method.

本文言語English
ページ(範囲)1-32
ページ数32
ジャーナルAnalysis and PDE
8
1
DOI
出版ステータスPublished - 2015

ASJC Scopus subject areas

  • 分析
  • 数値解析
  • 応用数学

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