Necessary and sufficient conditions for solvability of the Lewy equation

AUTOR(ES)

Greiner, P. C.

RESUMO

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 R3 is realized as the boundary of the generalized “upper-half-space” in C2, then the conditions are, near a point P [unk] R3, 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.

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