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Consumer optimization and a first-order PDE with a non-smooth system. (English) Zbl 1481.35126

Summary: We study a first-order nonlinear partial differential equation and present a necessary and sufficient condition for the global existence of its solution in a non-smooth environment. Using this result, we prove a local existence theorem for a solution to this differential equation. Moreover, we present two applications of this result. The first concerns an inverse problem called the integrability problem in microeconomic theory and the second concerns an extension of Frobenius’ theorem.

MSC:

35F25 Initial value problems for nonlinear first-order PDEs
57R30 Foliations in differential topology; geometric theory
49N45 Inverse problems in optimal control
91B16 Utility theory
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