Necessary and sufficient conditions for solvability of the Lewy equation | Zendy

Peter Greiner | Zendy; J. J. Kohn | Zendy; E. M. Stein | Zendy

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Necessary and sufficient conditions for solvability of the Lewy equation

Author(s) -

Peter Greiner,

J. J. Kohn,

E. M. Stein

Publication year - 1975

Publication title -

proceedings of the national academy of sciences

Language(s) - English

Resource type - Journals

SCImago Journal Rank - 5.011

H-Index - 771

eISSN - 1091-6490

pISSN - 0027-8424

DOI - 10.1073/pnas.72.9.3287

Subject(s) - mathematics , space (punctuation) , mathematical analysis , cauchy distribution , boundary value problem , combinatorics , pure mathematics , computer science , operating system

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 pointP [unk] R3 , the analytic continuability of the Cauchy-Szegö integral off pastP . In case the sufficient condition is satisfied, solutions are found that satisfy optimal regularity properties. Various generalizations are also given.

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