Document Type

Article

Publication Date

10-2-2013

Abstract

In this paper we give necessary and sufficient conditions for the existence of solutions to quasilinear equations of Lane-Emden type with measure data on a Carnot group G of arbitrary step. The quasilinear part involves operators of the p-Laplacian type ΔG, p, 1 < p < ∞. These results are based on new a priori estimates of solutions in terms of nonlinear potentials of Th. Wolff's type. As a consequence, we characterize completely removable singularities, and we prove a Liouville type theorem for supersolutions of quasilinear equations with source terms which has been known only for equations involving the sub-Laplacian (p = 2) on the Heisenberg group. © 2013 American Mathematical Society.

Publication Source (Journal or Book title)

Transactions of the American Mathematical Society

First Page

6569

Last Page

6593

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