Hölder Regularity up to the Boundary for Critical SQG on Bounded Domains

Journal Article (Journal Article)

We consider the dissipative SQG equation in bounded domains, first introduced by Constantin and Ignatova in 2016. We show global Hölder regularity up to the boundary of the solution, with a method based on the De Giorgi techniques. The boundary introduces several difficulties. In particular, the Dirichlet Laplacian is not translation invariant near the boundary, which leads to complications involving the Riesz transform.

Full Text

Duke Authors

Cited Authors

  • Stokols, LF; Vasseur, AF

Published Date

  • June 1, 2020

Published In

Volume / Issue

  • 236 / 3

Start / End Page

  • 1543 - 1591

Electronic International Standard Serial Number (EISSN)

  • 1432-0673

International Standard Serial Number (ISSN)

  • 0003-9527

Digital Object Identifier (DOI)

  • 10.1007/s00205-020-01498-3

Citation Source

  • Scopus