Necessary and sufficient conditions for solvability of the Lewy equation.
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.
Department of Mathematics, University of Toronto, Toronto, Canada M5S 1A1.
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Greiner
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Kohn
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Stein