Work

Global Hypoellipticity for a Class of Complex-Valued Evolution Equations on Compact Lie Groups

Year: 2026

Type: article

Abstract: We present necessary and sufficient conditions to have global hypoellipticity for a class of complex-valued coefficient first-order evolution equations defined on $$\mathbb {T}^1 \times G$$ T 1 × 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 $$(\mathcal {P})$$ ( P ) .

Source: Mediterranean Journal of Mathematics

DOI: 10.1007/s00009-026-03112-4

Author: Wagner Augusto Almeida de Moraes

Institution: Universidade Federal do Paraná

Language: English

Topic: Differential Equations and Boundary Problems

Subfield: Applied Mathematics

Field: Mathematics

Domain: Physical Sciences

Open Access status: hybrid

Estimated APC paid: $3,190

Funder: Conselho Nacional de Desenvolvimento Científico e Tecnológico