Regularity of solutions to a Vekua-type equation on compact Lie groups

Abstract

We present sufficient conditions to have global hypoellipticity for a class of Vekua-type operators defined on a compact Lie group. When the group has the property that every non-trivial representation is not self-dual we show that these sufficient conditions are also necessary. We also present results about the global solvability for this class of operators.

Global hypoellipticity for strongly invariant operators

“…Additional insights about solvability on the torus can be obtained in [1,2,3,8,14] and related works. In the broader context of compact Lie groups, some initial results are presented in [7,9,10]. Additional references regarding infinitesimal deformations of surfaces connected with solvability of Vekua-type operators include [6,12,13] and references therein…”