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DISTINCT SOLUTIONS TO GENERATED JACOBIAN EQUATIONS CANNOT INTERSECT

Part of: Elliptic equations and systems

Published online by Cambridge University Press:  20 February 2020

CALE RANKIN Open the ORCID record for CALE RANKIN [Opens in a new window]
CALE RANKIN*
Affiliation:
Mathematical Sciences Institute, Australian National University, Canberra, ACT 2601, Australia email cale.rankin@anu.edu.au
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Abstract

We prove that if two $C^{1,1}(\unicode[STIX]{x1D6FA})$ solutions of the second boundary value problem for the generated Jacobian equation intersect in $\unicode[STIX]{x1D6FA}$ then they are the same solution. In addition, we extend this result to $C^{2}(\overline{\unicode[STIX]{x1D6FA}})$ solutions intersecting on the boundary, via an additional convexity condition on the target domain.

Keywords

Jacobian equationsMonge–Ampère equationsuniqueness

MSC classification

Primary: 35J60: Nonlinear elliptic equations
Secondary: 35J96: Elliptic Monge-Ampère equations
Type
Research Article
Information
Bulletin of the Australian Mathematical Society , Volume 102 , Issue 3 , December 2020 , pp. 462 - 470
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Copyright
© 2020 Australian Mathematical Publishing Association Inc.

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Footnotes

This research is supported by an Australian Government Research Training Program (RTP) Scholarship.

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