Global hypoellipticity for a class of complex-valued evolution equations on compact Lie groups

2024/02/07 by de Moraes, Wagner A. A.
#43A77 #58D25 #Analysis of PDEs (math.AP) #FOS: Mathematics #Primary 35F05 #Secondary 35B10

paper · doi:10.48550/arxiv.2402.04950

Abstract

We present necessary and sufficient conditions to have global hypoellipticity for a class of complex-valued coefficient first order evolution equations defined on \mathbbT¹ × G, where G is a compact Lie group. First, we show that the global hypoellipticity of the constant coefficient operator related to this operator is a necessary condition, but not a sufficient condition. Under certain hypothesis, we show that the global hypoellipticity of this class of operator is completely characterized by Nirenberg-Treves' condition (P).

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