Annales Academiæ Scientiarum Fennicæ
Mathematica
Volumen 39, 2014, 605-623

THE PARABOLIC p-LAPLACE EQUATION IN CARNOT GROUPS

Thomas Bieske and Erin Martin

University of South Florida, Department of Mathematics and Statistics
4202 E. Fowler Ave. CMC342, Tampa, FL 33620, U.S.A.; tbieske 'at' usf.edu

Westminster College, Department of Mathematical Sciences
501 Westminster Ave, Fulton, MO 65251, U.S.A.; Erin.Martin 'at' westminster-mo.edu

Abstract. By establishing a parabolic maximum principle, we show uniqueness of viscosity solutions to the parabolic p-Laplace equation and then examine the limit as t goes to infinity. Additionally, we explore the limit as p goes to infinity.

2010 Mathematics Subject Classification: Primary 53C17, 35K65, 35D40; Secondary 35H20, 22E25, 17B70.

Key words: Parabolic p-Laplace equation, viscosity solution, Carnot groups.

Reference to this article: T. Bieske and E. Martin: The parabolic p-Laplace equation in Carnot groups. Ann. Acad. Sci. Fenn. Math. 39 (2014), 605-623.

Full document as PDF file

doi:10.5186/aasfm.2014.3928