First-order linear PDE’s and uniqueness in the Cauchy problem. (English) Zbl 0266.35009


35A05 General existence and uniqueness theorems (PDE) (MSC2000)
35F10 Initial value problems for linear first-order PDEs
Full Text: DOI


[1] Hörmander, L., Linear Partial Differential Operators (1963), Springer: Springer New York · Zbl 0171.06802
[2] Nirenberg, L.; Treves, F., Solvability of a first order linear partial differential equation, Comm. Pure Appl. Math., 16, 331-351 (1963) · Zbl 0117.06104
[3] Nirenberg, L.; Treves, F., On local solvability of linear partial differential equations— Part II: Sufficient conditions, Comm. Pure Appl. Math., 23, 459-510 (1970) · Zbl 0208.35902
[4] Treves, F., Linear Partial Differential Equations with Constant Coefficients (1967), Gordon & Breach: Gordon & Breach New York
[5] Treves, F., Ovcyannikov theorem and hyperdifferential operators, Notas de Matematica, No. 46 (1968), Rio de Janeiro · Zbl 0205.39202
[6] Treves, F., Hypoelliptic partial differential equations of principal type. Sufficient conditions and necessary conditions, Comm. Pure Appl. Math., 24, 631-670 (1971) · Zbl 0234.35019
[7] Treves, F., A link between solvability of pseudodifferential equations and uniqueness in the Cauchy problem, Amer. J. Math., 94, 267-288 (1972) · Zbl 0274.35054
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.