Doubly Nonlinear Equations as Convex Minimization
Doubly Nonlinear Equations as Convex Minimization
We present a variational reformulation of a class of doubly nonlinear parabolic equations as (limits of) constrained convex minimization problems. In particular, an $\varepsilon$-dependent family of weighted energy-dissipation (WED) functionals on entire trajectories is introduced and proved to admit minimizers. These minimizers converge to solutions of the original doubly nonlinear …