zbMATH — the first resource for mathematics

Comparison principle for parabolic equations in the Heisenberg group. (English) Zbl 1085.35014
Author’s abstract: We define two notions of viscosity solutions to parabolic equations in the Heisenberg group, depending on whether the test functions concern only the past or both and the future. We then exploit the Heisenberg geometry to prove a comparison principle for a class of parabolic equations and show the sufficiency of considering the test functions that concern only the past.
Reviewer: Jiaqi Mo (Wuhu)

35B05 Oscillation, zeros of solutions, mean value theorems, etc. in context of PDEs
35K55 Nonlinear parabolic equations
22E25 Nilpotent and solvable Lie groups
Full Text: EuDML EMIS