DISTINCT SOLUTIONS TO GENERATED JACOBIAN EQUATIONS CANNOT INTERSECT

2020/02/11 by Cale Rankin, CALE RANKIN · 5 citations
Mathematics · Physics and Astronomy · #Advanced Differential Equations and Dynamical Systems #Boundary (topology) #Boundary value problem #Convexity #Initial value problem #Jacobian matrix and determinant #Nonlinear Differential Equations Analysis #Nonlinear Waves and Solitons #math.AP

paper · pdf · open access · doi:10.1017/s0004972720000052

published in Bulletin of the Australian Mathematical Society 102(3), 462-470 (Cambridge University Press) · Submitted Bulletin of the Australian Mathematical Society November 2019. Accepted December 2019

arxiv created 2020/02/11 · openalex publication_date 2020/02/20 · openalex created_date 2020/02/24 · arxiv updated 2020/11/25 · openalex updated_date 2026/08/05

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 C²(\unicode[STIX]x1D6FA) solutions intersecting on the boundary, via an additional convexity condition on the target domain.

Citations

• Elliptic Partial Differential Equations of Second Order
• Measure Theory and Fine Properties of Functions, Revised Edition

Cited by

• Strict convexity and C¹ regularity of solutions to generated Jacobian equations in dimension two