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

Seiichiro Kusuoka

Research output: Contribution to journalArticle

7 Citations (Scopus)


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.

Original languageEnglish
Pages (from-to)1-32
Number of pages32
JournalAnalysis and PDE
Issue number1
Publication statusPublished - Jan 1 2015



  • Coupling method
  • Diffusion
  • Fundamental solution
  • Gaussian estimate
  • Hölder continuity
  • Parabolic partial differential equation
  • Stochastic differential equation

ASJC Scopus subject areas

  • Analysis
  • Numerical Analysis
  • Applied Mathematics

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