|
|||||
 |
|
|
|
|
|
|
Carleson measure
estimates for caloric functions and parabolic uniformly
rectifiable sets
Simon Bortz, John Hoffman, Steve Hofmann, José Luis Luna García and Kaj Nyström |
|
Vol. 16 (2023), No. 4, 1061–1088
|
 |
Abstract |
|
|
Let be a parabolic uniformly rectifiable set. We prove that every bounded solution to satisfies a Carleson measure estimate condition. An important technical novelty of our work is that we develop a corona domain approximation scheme for in terms of regular graph domains. This scheme has an analogous elliptic version which improves on the known results in that setting. |
Keywords
parabolic equations, parabolic uniform rectifiability,
Carleson measures
|
Mathematical Subject Classification
Primary: 28A75
Secondary: 28A78, 35K10, 42B37
|
Milestones
Received: 29 March 2021
Revised: 23 September 2021
Accepted: 26 October 2021
Published: 15 June 2023
|
Authors |
| Simon Bortz | |
| Department of Mathematics University of Alabama Tuscaloosa, AL United States |
|
| John Hoffman | |
| Department of Mathematics University of Missouri at Columbia Columbia, MO United States |
|
| Steve Hofmann | |
| Department of Mathematics University of Missouri at Columbia Columbia, MO United States |
|
| José Luis Luna García | |
| Department of Mathematics &
Statistics McMaster University Hamilton Canada |
|
| Kaj Nyström | |
| Department of Mathematics Uppsala University Uppsala Sweden |
|
| © 2023 MSP (Mathematical Sciences Publishers). Distributed under the Creative Commons Attribution License 4.0 (CC BY). |
Open Access made possible by participating institutions via Subscribe to Open.
