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DISTINCT SOLUTIONS TO GENERATED JACOBIAN EQUATIONS CANNOT INTERSECT

Published online by Cambridge University Press:  20 February 2020

CALE RANKIN
Affiliation:
Mathematical Sciences Institute, Australian National University, Canberra, ACT 2601, Australia email cale.rankin@anu.edu.au
Corresponding
E-mail address:

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.

Type
Research Article
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.

References

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DISTINCT SOLUTIONS TO GENERATED JACOBIAN EQUATIONS CANNOT INTERSECT
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