Necessary and sufficient conditions for solvability of the Lewy equation - Greiner, P. C. (1975)
We find the necessary and sufficient conditions for the local solvability of Lewy's equation, ([unk]/[unk]z + īz [unk]/[unk]t) u = f. If R(3) is realized as the boundary of the generalized “upper-half-space” in C(2), then the conditions are, near a point P [unk] R(3), the analytic continuability of the Cauchy-Szegö integral of f past P. In case the sufficient condition is satisfied, solutions are found that satisfy optimal regularity properties. Various generalizations are also given.