WedevelopanelementarymethodtogiveaLipschitzestimateforthemin- imizers in the problem of Herglotz’ variational principle proposed in [17] in the time- dependent case. We deduce Erdmann’s condition and the Euler-Lagrange equation sep- arately under different sets of assumptions, by using a generalized du Bois-Reymond lemma. As an application, we obtain a representation formula for the viscosity solution of the Cauchy problem for the Hamilton-Jacobi equation Dtu(t, x) + H(t, x, Dxu(t, x), u(t, x)) = 0 and study the related Lax-Oleinik evolution.
Cannarsa, P., Cheng, W., Jin, L., Wang, K., Yan, J. (2020). Herglotz' variational principle and Lax-Oleinik evolution. JOURNAL DE MATHÉMATIQUES PURES ET APPLIQUÉES, 141, 99-136 [10.1016/j.matpur.2020.07.002].
Herglotz' variational principle and Lax-Oleinik evolution
Cannarsa, Piermarco;
2020-01-01
Abstract
WedevelopanelementarymethodtogiveaLipschitzestimateforthemin- imizers in the problem of Herglotz’ variational principle proposed in [17] in the time- dependent case. We deduce Erdmann’s condition and the Euler-Lagrange equation sep- arately under different sets of assumptions, by using a generalized du Bois-Reymond lemma. As an application, we obtain a representation formula for the viscosity solution of the Cauchy problem for the Hamilton-Jacobi equation Dtu(t, x) + H(t, x, Dxu(t, x), u(t, x)) = 0 and study the related Lax-Oleinik evolution.| File | Dimensione | Formato | |
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