Journal of Convex Analysis 32 (2025), No. 3, 653--660
Copyright Heldermann Verlag 2025
Hamilton-Jacobi Theory in the Calculus of Variations Under Partial Convexity Assumptions on the Lagrangian
Jean-Paul Penot
Sorbonne Universitées, UPMC Université Paris, France
penotjp64@gmail.com
Using general results about subdifferentials of value functions, under partial convexity assumptions on the Lagrangian, we derive the main result about the Hamilton-Jacobi theory in the calculus of variations obtained by R. T. Rockafellar and P. Wolenski [Convexity in Hamilton-Jacobi theory, SIAM J. Control Optimization 39/5 (2000) 1323--1372] under full convexity of the Lagrangian. Since a number of results in the calculus of variations are known to be valid under such an assumption, it is tempting to tackle such an aim, even if the nice duality theory presented in the work cited above seems to be out of reach.
Keywords: Subdifferential, value function, partial convexity, Lagrangian, Hamilton-Jacobi theory, calculus of variations.
MSC: 49L99, 90C25.
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