On systems of first order linear partial differential equations with \(L^p\) coefficients. (English) Zbl 1152.35334

Summary: We establish the existence, the uniqueness, and the stability of the solution to the Cauchy problem associated to a general class of systems of first-order linear partial differential equations under minimal regularity assumptions on their coefficients.


35F10 Initial value problems for linear first-order PDEs
35N10 Overdetermined systems of PDEs with variable coefficients
58A17 Pfaffian systems
35R05 PDEs with low regular coefficients and/or low regular data