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Normalization of complex-valued planar vector fields which degenerate along a real curve. (English) Zbl 1129.35419
Summary: Taking as a start point the recent article of A. Meziani [J. Funct. Anal. 179, No. 2, 333–373 (2001; Zbl 0973.35083)], we present several results concerning the normalization of a class of complex vector fields in the plane which degenerate along a real curve. We mainly deal with operators with finite regularity and analyze both the local situation as well as the case of normalization near a circle. Some related questions (e.g., on semi-global solvability and on the normalization of a class of generalized Mizohata operators) are also discussed.

35J70 Degenerate elliptic equations
35A20 Analyticity in context of PDEs
37G05 Normal forms for dynamical systems
Full Text: DOI
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