Green’s function for second order parabolic equations with singular lower order coefficients

Seick Kim, Longjuan Xu

Research output: Contribution to journalArticlepeer-review

1 Citation (Scopus)

Abstract

We construct Green’s functions for second order parabolic operators of the form Pu = ∂tu−div(A∇u+bu)+c·∇u+du in (−∞, ∞)×Ω, where Ω is an open connected set in Rn. It is not necessary that Ω to be bounded and Ω = Rn is not excluded. We assume that the leading coefficients A are bounded and measurable and the lower order coefficients b, c, and d belong to critical mixed norm Lebesgue spaces and satisfy the conditions d − divb ≥ 0 and div(b−c) ≥ 0. We show that the Green’s function has the Gaussian bound in the entire (−∞, ∞) × Ω.

Original languageEnglish
Pages (from-to)1-21
Number of pages21
JournalCommunications on Pure and Applied Analysis
Volume21
Issue number1
DOIs
Publication statusPublished - 2022 Jan

Bibliographical note

Funding Information:
S. Kim was partially supported by the National Research Foundation of Korea under agreements NRF-2019R1A2C2002724 and NRF-20151009350. ∗ Corresponding author.

Publisher Copyright:
© 2022 American Institute of Mathematical Sciences. All rights reserved.

All Science Journal Classification (ASJC) codes

  • Analysis
  • Applied Mathematics

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