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We provide relaxation for not lower semicontinuous supremal functionals of the type $W^{1,infty}(Omega;mathbb R^d) i u mapstosupess_{ x in Omega}f( abla u(x))$ in the vectorial case, where $Omegasubset mathbb R^N$ is a Lipschitz, bounded open set, and $f$ is level convex. The connection with indicator functionals is also enlightened, thus extending previous lower semicontinuity results in that framework. Finally we discuss the $L^p$-approximation of supremal functionals, with non-negative, coercive densities $f=f(x,xi)$, which are only $L^N otimes B_{d times N}$-measurable.
We study variational problems involving nonlocal supremal functionals $L^infty(Omega;mathbb{R}^m) i umapsto {rm ess sup}_{(x,y)in Omegatimes Omega} W(u(x), u(y)),$ where $Omegasubset mathbb{R}^n$ is a bounded, open set and $W:mathbb{R}^mtimesmat
Consider the Landau equation with Coulomb potential in a periodic box. We develop a new $L^{2}rightarrow L^{infty }$ framework to construct global unique solutions near Maxwellian with small $L^{infty } $norm. The first step is to establish global $L
An optimal control problem with a time-parameter is considered. The functional to be optimized includes the maximum over time-horizon reached by a function of the state variable, and so an $L^infty$-term. In addition to the classical control function
Avikainen showed that, for any $p,q in [1,infty)$, and any function $f$ of bounded variation in $mathbb{R}$, it holds that $mathbb{E}[|f(X)-f(widehat{X})|^{q}] leq C(p,q) mathbb{E}[|X-widehat{X}|^{p}]^{frac{1}{p+1}}$, where $X$ is a one-dimensional r
Riemannian cubics are critical points for the $L^2$ norm of acceleration of curves in Riemannian manifolds $M$. In the present paper the $L^infty$ norm replaces the $L^2$ norm, and a less direct argument is used to derive necessary conditions analogo