We consider variational solutions to the Cauchy-Dirichlet problem∂ tu= div D ξ f (x, u, D u)−
D uf (x, u, D u) in Ω T u= u 0 on∂ par Ω T where the function f= fx, u, ξ, f: R n× RN× RN× …

In this paper we introduce a purely variational approach to time dependent problems,
yielding the existence of global parabolic minimizers, that is∫ 0 T∫ Ω [u⋅∂ t φ+ f (x, D u)] …

In this paper we introduce a purely variational approach to the gradient flows, naturally
arising in image denoising models, yielding the existence of global parabolic minimizers, in …

We present a variational reformulation of a class of doubly nonlinear parabolic equations as
(limits of) constrained convex minimization problems. In particular, an ε-dependent family of …

Partial Differential Equations — A variational approach to doubly nonlinear equations, by
Verena Bögelein, Frank Duzaar, Paol Page 1 Rend. Lincei Mat. Appl. 29 (2018), 739–772 DOI …

We present a novel variational view at Lagrangian mechanics based on the minimization of
weighted inertia-energy functionals on trajectories. In particular, we introduce a family of …

This paper develops the so-called Weighted Energy-Dissipation (WED) variational approach
for the analysis of gradient flows in metric spaces. This focuses on the minimization of the …

Develo** an original idea of De Giorgi, we introduce a new and purely variational
approach to the Cauchy Problem for a wide class of defocusing hyperbolic equations. The …

We prove uniform parabolic Hölder estimates of De Giorgi–Nash–Moser type for sequences
of minimizers of the functionals E ε (W)=∫ 0∞ et/ε ε {∫ R+ N+ 1 ya ε|∂ t W| 2+|∇ W| 2 d …

This paper focuses on the so-called weighted inertia-dissipation-energy variational
approach for the approximation of unsteady Leray–Hopf solutions of the incompressible …