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Darboux Theorem and Ellipticity

MSRI / SLMath 40th Anniversary Symposium April 13, 2023 - April 14, 2023

April 14, 2023 (10:30 AM PDT - 11:30 AM PDT)
Speaker(s): WILFRID GANGBO (University of California, Los Angeles)
Location: SLMath: Eisenbud Auditorium, Online/Virtual
Primary Mathematics Subject Classification No Primary AMS MSC
Secondary Mathematics Subject Classification No Secondary AMS MSC
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Darboux Theorem And Ellipticity

Abstract

We identify a maximal system of equations which renders the classical Darboux problem elliptic, thereby providing a selection criterion for its well posedness. As a byproduct, we obtain, what we term symplectic factorization of vector fields: any map u, satisfying appropriate assumptions, can be factored as: u = χ◦ψ with ψ∗(ωm) = ωm,dχ[; ωm
= 0 and ∇χ+(∇χ)t > 0. Here, ωm is the standard symplectic form on R2m,] is the musical isomorphism and [ its inverse. (This talk is based on a joint work with B. Dacorogna and O. Kneuss)

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Darboux Theorem And Ellipticity

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