Consumer Optimization and a First-Order PDE with a Non-Smooth System

Yuhki Hosoya ()
Additional contact information
Yuhki Hosoya: Chuo University

SN Operations Research Forum, 2021, vol. 2, issue 4, 1-36

Abstract: Abstract 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.

Keywords: Non-smooth partial differential equation; Rademacher’s theorem; Global existence; Frobenius’ theorem; Consumer theory; Integrability theory; 35F25; 57R30; 49N45; 91B16 (search for similar items in EconPapers)
Date: 2021
References: View references in EconPapers View complete reference list from CitEc
Citations: View citations in EconPapers (3)

Downloads: (external link)
http://link.springer.com/10.1007/s43069-021-00104-w Abstract (text/html)
Access to the full text of the articles in this series is restricted.

Related works:
This item may be available elsewhere in EconPapers: Search for items with the same title.

Export reference: BibTeX RIS (EndNote, ProCite, RefMan) HTML/Text

Persistent link: https://EconPapers.repec.org/RePEc:spr:snopef:v:2:y:2021:i:4:d:10.1007_s43069-021-00104-w

Ordering information: This journal article can be ordered from
https://www.springer.com/journal/43069

DOI: 10.1007/s43069-021-00104-w

Access Statistics for this article

SN Operations Research Forum is currently edited by Marco Lübbecke

More articles in SN Operations Research Forum from Springer
Bibliographic data for series maintained by Sonal Shukla () and Springer Nature Abstracting and Indexing ().