This article is cited in 10 papers

Local solvability of pseudodifferential operators with characteristics of second multiplicity

P. R. Popivanov


Abstract: A study is made of the local properties of operators whose leading symbol admits a representation in the form of a sum (difference) of squares of operators of principal type. The coefficients are infinitely smooth and are not necessarily of power growth. Necessary and sufficient conditions are formulated in the invariant language of null bicharacteristics and of the subprincipal symbol. Definitive results are obtained for some special classes of equations. The work extends results obtained earlier by the author for operators whose leading symbol is the square of an operator of principal type.
Bibliography: 27 titles.

UDC: 517.43

MSC: 35S05, 47G05

Received: 10.02.1975

 English version: Mathematics of the USSR-Sbornik, 1976, 29:2, 193–216

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