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DISTINCT SOLUTIONS TO GENERATED JACOBIAN EQUATIONS CANNOT INTERSECT
Part of
- Elliptic equations and systems
CALE RANKIN
Journal:

Bulletin of the Australian Mathematical Society / Volume 102 / Issue 3 / December 2020

Published online by Cambridge University Press:

20 February 2020, pp. 462-470

Print publication:

December 2020
- Article
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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.