Local C 0,1 -Regularity for the Parabolic p -Laplacian Equation on the Group SU(3)

Yongming He, Chengwei Yu () and Hongqing Wang
Additional contact information
Yongming He: Department of Basic, China Fire and Rescue Institue, 4 Nanyan Road, Changping District, Beijing 102202, China
Chengwei Yu: Department of Basic, China Fire and Rescue Institue, 4 Nanyan Road, Changping District, Beijing 102202, China
Hongqing Wang: Department of Basic, China Fire and Rescue Institue, 4 Nanyan Road, Changping District, Beijing 102202, China

Mathematics, 2024, vol. 12, issue 9, 1-20

Abstract: In this article, when 2 ≤ p ≤ 4 , we establish the C loc 0 , 1 -regularity of weak solutions to the degenerate parabolic p -Laplacian equation ∂ t u = − ∑ i = 1 6 X i * ( | ∇ H u | p − 2 X i u ) on the group SU(3) granted with horizontal vector fields X 1 , … , X 6 . Compared to the Heisenberg group, H n , we obtained the optimal range of p ; that is, 2 ≤ p ≤ 4 .

Keywords: p -Laplacian type; C loc 0 , 1 -regularity; parabolic p -Laplacian; the group SU(3); range of p; Caccioppoli-type inequality (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2024
References: View complete reference list from CitEc
Citations:

Downloads: (external link)
https://www.mdpi.com/2227-7390/12/9/1288/pdf (application/pdf)
https://www.mdpi.com/2227-7390/12/9/1288/ (text/html)

Related works:
This item may be available elsewhere in EconPapers: Search for items with the same title.

Export reference: BibTeX RIS (EndNote, ProCite, RefMan) HTML/Text

Persistent link: https://EconPapers.repec.org/RePEc:gam:jmathe:v:12:y:2024:i:9:p:1288-:d:1381983

Access Statistics for this article

Mathematics is currently edited by Ms. Emma He

More articles in Mathematics from MDPI
Bibliographic data for series maintained by MDPI Indexing Manager ().