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

Seiichiro Kusuoka

Research output: Contribution to journalArticle

7 Citations (Scopus)

Abstract

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
Volume8
Issue number1
DOIs
Publication statusPublished - 2015
Externally publishedYes

Fingerprint

Fundamental Solution
Partial differential equations
Parabolic Equation
Coupling Method
Parabolic Partial Differential Equations
Coefficient
Diffusion Process
Necessary
Form

Keywords

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

ASJC Scopus subject areas

  • Analysis
  • Applied Mathematics
  • Numerical Analysis

Cite this

Hölder continuity and bounds for fundamental solutions to nondivergence form parabolic equations. / Kusuoka, Seiichiro.

In: Analysis and PDE, Vol. 8, No. 1, 2015, p. 1-32.

Research output: Contribution to journalArticle

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