Necessary and sufficient conditions for solvability of the Lewy equation
- 1 September 1975
- journal article
- Published by Proceedings of the National Academy of Sciences in Proceedings of the National Academy of Sciences
- Vol. 72 (9) , 3287-3289
- https://doi.org/10.1073/pnas.72.9.3287
Abstract
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.Keywords
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