Geodesic
Lipschitz regularity for solutions of the parabolic p-Laplacian in the Heisenberg group
Luca Capogna1 ; Giovanna Citti2 ; Xiao Zhong3
1 Smith College, Department of Mathematics and Statistics
2 Università di Bologna, Dipartimento di Matematica, and Accademia dei Lincei, Centro Linceo interdisciplinare Beniamino Segre
3 University of Helsinki, Department of Mathematics and Statistics
Annales Fennici Mathematici, Tome 48 (2023) no. 2, pp. 411-428.

Voir la notice de l'article provenant de la source Journal.fi

We prove local Lipschitz regularity for weak solutions to a class of degenerate parabolic PDEs modeled on the parabolic $p$-Laplacian $\partial_t u= \sum_{i=1}^{2n} X_i (|\nabla_0 u|^{p-2} X_i u),$in a cylinder $\Omega\times\mathbb{R}^+$, where $\Omega$ is domain in the Heisenberg group $\mathbb{H}^n$, and $2\le p \le 4$. The result continues to hold in the more general setting of contact subRiemannian manifolds.  
DOI : 10.54330/afm.131227
Keywords: Subelliptic p-Laplacian, parabolic gradient estimates, Heisenberg group

Luca Capogna 1 ; Giovanna Citti 2 ; Xiao Zhong 3

1 Smith College, Department of Mathematics and Statistics
2 Università di Bologna, Dipartimento di Matematica, and Accademia dei Lincei, Centro Linceo interdisciplinare Beniamino Segre
3 University of Helsinki, Department of Mathematics and Statistics 
@article{AFM_2023_48_2_a0,
     author = {Luca Capogna and Giovanna Citti and Xiao Zhong},
     title = {Lipschitz regularity for solutions of the parabolic {p-Laplacian} in the {Heisenberg} group},
     journal = {Annales Fennici Mathematici},
     pages = {411--428},
     publisher = {mathdoc},
     volume = {48},
     number = {2},
     year = {2023},
     doi = {10.54330/afm.131227},
     language = {en},
     url = {http://geodesic.mathdoc.fr/articles/10.54330/afm.131227/}
}
TY  - JOUR
AU  - Luca Capogna
AU  - Giovanna Citti
AU  - Xiao Zhong
TI  - Lipschitz regularity for solutions of the parabolic p-Laplacian in the Heisenberg group
JO  - Annales Fennici Mathematici
PY  - 2023
SP  - 411
EP  - 428
VL  - 48
IS  - 2
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/articles/10.54330/afm.131227/
DO  - 10.54330/afm.131227
LA  - en
ID  - AFM_2023_48_2_a0
ER  - 
%0 Journal Article
%A Luca Capogna
%A Giovanna Citti
%A Xiao Zhong
%T Lipschitz regularity for solutions of the parabolic p-Laplacian in the Heisenberg group
%J Annales Fennici Mathematici
%D 2023
%P 411-428
%V 48
%N 2
%I mathdoc
%U http://geodesic.mathdoc.fr/articles/10.54330/afm.131227/
%R 10.54330/afm.131227
%G en
%F AFM_2023_48_2_a0
Luca Capogna; Giovanna Citti; Xiao Zhong. Lipschitz regularity for solutions of the parabolic p-Laplacian in the Heisenberg group. Annales Fennici Mathematici, Tome 48 (2023) no. 2, pp. 411-428. doi : 10.54330/afm.131227. http://geodesic.mathdoc.fr/articles/10.54330/afm.131227/

Cité par Sources :