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A class of planar vector fields with homogeneous singular points: solvability and boundary value problems. (English) Zbl 1397.35066
Summary: This paper deals with the solvability of planar complex vector fields with homogeneous degeneracies. Hölder continuous solutions are obtained via a Cauchy type integral operator associated to the vector field. An associated boundary value problem of Riemann-Hilbert type is also considered.

35F15 Boundary value problems for linear first-order PDEs
35A01 Existence problems for PDEs: global existence, local existence, non-existence
35F05 Linear first-order PDEs
35C15 Integral representations of solutions to PDEs
35J70 Degenerate elliptic equations
35Q15 Riemann-Hilbert problems in context of PDEs
Full Text: DOI
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