Heat flow for extremal functions in some subcritical sobolev inequalities

Abstract

We study here the global existence of solutions for a heat flow involving extremal functions in some subcritical Sobolev inequalities. We prove in this paper that such solutions exist at all time by a finite differences method.

Keywords:

• Evolution Equations
• Sobolev inequalities
• Finite differences method
• Parabolic p-Laplacian

AMS Subject Classification:

• 35K55
• 35K65
• 49J45

^* BruNo. [email protected]

^* BruNo. [email protected]

Notes

^* BruNo. [email protected]