Abstract
AbstractWe 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.
Funder
japan society for the promotion of science
Japan Society for the Promotion of Science
Publisher
Springer Science and Business Media LLC
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