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A study of comparison, existence and regularity of viscosity and weak solutions for quasilinear equations in the Heisenberg group

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The authors are supported by grants PICT 2015-1701 AGENCIA, and SECTyP UNCuyo B051

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  • 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.

    Mathematics Subject Classification: Primary: 35R03, 49L25, 35B51; Secondary: 35D540, 35D30.

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