CPAA
A study of comparison, existence and regularity of viscosity and weak solutions for quasilinear equations in the Heisenberg group
Pablo Ochoa Julio Alejo Ruiz
Communications on Pure & Applied Analysis 2019, 18(3): 1091-1115 doi: 10.3934/cpaa.2019053

In this manuscript, we are interested in the study of existence, uniqueness and comparison of viscosity and weak solutions for quasilinear equations in the Heisenberg group. In particular, we highlight the limitation of applying the Euclidean theory of viscosity solutions to get comparison of solutions of sub-elliptic equations in the Heisenberg group. Moreover, we will be concerned with the equivalence of different notions of weak solutions under appropriate assumptions for the operators under analysis. We end the paper with an application to a Radó property.

keywords: Partial differential equations on the Heisenberg group viscosity solutions comparison principle weak solutions Radó type theorem

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