On C1/2,1 , C1,2 , and C, estimates for linear parabolic operators

Hongjie Dong, Luis Escauriaza, Seick Kim

Research output: Contribution to journalArticlepeer-review

2 Citations (Scopus)


We show that weak solutions to parabolic equations in divergence form with zero Dirichlet boundary conditions are continuously differentiable up to the boundary when the leading coefficients have Dini mean oscillation and the lower-order coefficients verify certain conditions. Analogous results are obtained for non-divergence form parabolic operators and their adjoint operators. Under similar conditions, we also establish a Harnack inequality for nonnegative adjoint solutions, together with upper and lower Gaussian bounds for the global fundamental solution.

Original languageEnglish
Pages (from-to)4641-4702
Number of pages62
JournalJournal of Evolution Equations
Issue number4
Publication statusPublished - 2021 Dec

Bibliographical note

Funding Information:
S. Kim is supported by NRF Grant No. NRF-20151009350 and No. NRF-2019R1A2C2002724.

Funding Information:
L. Escauriaza is supported by Basque Government grant IT1247-19 and MICINN grant PGC2018-094522-B-I00.

Funding Information:
H. Dong was partially supported by the NSF under agreement DMS-1600593.

Publisher Copyright:
© 2021, The Author(s), under exclusive licence to Springer Nature Switzerland AG.

All Science Journal Classification (ASJC) codes

  • Mathematics (miscellaneous)


Dive into the research topics of 'On C1/2,1 , C1,2 , and C, estimates for linear parabolic operators'. Together they form a unique fingerprint.

Cite this