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Properties of solutions of a class of hypocomplex vector fields. (English) Zbl 1362.35088
Berhanu, Shiferaw (ed.) et al., Analysis and geometry in several complex variables. Workshop on analysis and geometry in several complex variables, Texas A&M University at Qatar, Doha, Qatar, January 4–8, 2015. Proceedings. Providence, RI: American Mathematical Society (AMS) (ISBN 978-1-4704-2255-4/pbk; 978-1-4704-3663-6/ebook). Contemporary Mathematics 681, 29-50 (2017).
Summary: A Cauchy type integral operator is associated to a class of integrable vector fields with complex coefficients. Properties of the integral operator are used to deduce Hölder solvability of semilinear equations \(Lu=F(x,y,u)\) and a strong similarity principle between the solutions of the equation \(Lu=au+b\overline {u}\) and those of the equation \(Lu=0\).
For the entire collection see [Zbl 1358.32003].

MSC:
35C15 Integral representations of solutions to PDEs
35F15 Boundary value problems for linear first-order PDEs
35M12 Boundary value problems for PDEs of mixed type
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