On the Euler-Lagrange equation for a variational problem: The general case. II

DOI10.1007/s00209-009-0547-2zbMath1221.49035OpenAlexW2119075035MaRDI QIDQ611988

Stefano Bianchini, Matteo Gloyer

Publication date: 3 January 2011

Published in: Mathematische Zeitschrift (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/s00209-009-0547-2

zbMATH Keywords

Hamilton-Jacobi equationEuler-Lagrange equationdisintegration of a measureextended valued functions

Mathematics Subject Classification ID

Optimality conditions for problems involving partial differential equations (49K20)

Related Items (10)

Transport Rays and Applications to Hamilton–Jacobi Equations ⋮ The Monge problem for strictly convex norms in \(\mathbb R^d\) ⋮ SBV-like regularity for Hamilton-Jacobi equations with a convex Hamiltonian ⋮ A nonhomogeneous boundary value problem in mass transfer theory ⋮ The Monge problem for distance cost in geodesic spaces ⋮ Finite volume schemes for the approximation via characteristics of linear convection equations with irregular data ⋮ Wasserstein barycenters over Riemannian manifolds ⋮ On Sudakov’s type decomposition of transference plans with norm costs ⋮ A proof of Sudakov theorem with strictly convex norms ⋮ The disintegration of the Lebesgue measure on the faces of a convex function

Cites Work

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• A geometrical approach to monotone functions in \(\mathbb{R}^n\)
• On the Euler-Lagrange Equation for a Variational Problem
• On the existence of variations, possibly with pointwise gradient constraints
• On the Validity of the Maximum Principle and of the Euler--Lagrange Equation for a Minimum Problem Depending on the Gradient

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