Related papers: Weak Capacity and Critical Exponents

We introduce a variational first-order Sobolev calculus on metric measure spacetimes. The key object is the maximal weak subslope of an arbitrary causal function, which plays the role of the (Lorentzian) modulus of its differential. It is…

Let $X$ be a Banach space and let $C$ be a closed convex bounded subset of $X$. It is proved that $C$ is weakly compact if, and only if, $C$ has the {it generic} fixed point property ($\mathcal{G}$-FPP) for the class of $L$-bi-Lipschitz…

We carry out a comprehensive study of quantitative homogenization of second-order elliptic systems with bounded measurable coefficients that are almost-periodic in the sense of H. Weyl. We obtain uniform local $L^2$ estimates for the…

A long-standing conjecture states that all normalized symplectic capacities coincide on the class of convex subsets of ${\mathbb R}^{2n}$. In this note we focus on an asymptotic (in the dimension) version of this conjecture, and show that…

This paper studies the properties of weak solutions to a class of space-time fractional parabolic-elliptic Keller-Segel equations with logistic source terms in $\mathbb{R}^{n}$, $n\geq 2$. The global existence and $L^{\infty}$-bound of weak…

A weak metric on a set is a function that satisfies the axioms of a metric except the symmetry and the separation axioms. In the present paper we introduced a weak metric, called the Apollonian weak metric, on any subset of a Euclidean…

We are concerned with quasilinear symmetrizable partially dissipative hyperbolic systems in the whole space $\mathbb{R}^d$ with $d\geq2$. Following our recent work [10] dedicated to the one-dimensional case, we establish the existence of…

On the two dimensional sphere, we consider axisymmetric critical points of an isoperimetric problem perturbed by a long-range interaction term. When the parameter controlling the nonlocal term is sufficiently large, we prove the existence…

In the present paper, we deal with a quasilinear elliptic equation involving a critical Sobolev exponent on non-compact Randers spaces. Under very general assumptions on the perturbation, we prove the existence of a non-trivial solution.…

We present several examples of fundamental problems involving weak continuity and compactness for nonlinear partial differential equations, in which compensated compactness and related ideas have played a significant role. We first focus on…

We present a weak measurement protocol that permits a sensitive estimation of angular rotations based on the concept of weak-value amplification. The shift in the state of a pointer, in both angular position and the conjugate orbital…

We define the notion of weak Minkowski metric and prove some basic properties of such metrics. We also highlight some of the important analogies between Minkowski geometry and the Funk and Hilbert geometries.

We derive sharp Adams inequalities for the Riesz and other potentials of functions with arbitrary compact support in R^n. Up to now such results were only known for a class of functions whose supports have uniformly bounded measure. We…

We prove two weak compactness criteria in Musielak-Orlicz spaces for $N$-functions satisfying the $\Delta_2$-condition. They extend criteria from And\^o for Orlicz spaces to this setting of non-symmetrical Banach function spaces. As…

Recently a restriction ("quantum inequality-type relation") on the (renormalized) energy density measured by a static observer in a "globally static" (ultrastatic) spacetime has been formulated by Pfenning and Ford for the minimally coupled…

This paper discusses generalized weak rigidity theory, and aims to apply the theory to formation control problems with a gradient flow law. The generalized weak rigidity theory is utilized in order that desired formations are characterized…

In this paper, we provide a direct proof for the equivalence of K.M. Chong's and De la Vall\'{e}e Poussin's criteria of weak compactness of a subset $K$ of $L_1(0,1)$ in terms of some Orlicz function. Furthermore, we discuss the equivalence…

This work examines the argument of weak values for general observables and develops a geometric description on the Bloch sphere. We apply the Majorana symmetric representation to reach this goal. The weak value of a general observable is…

We show that an Ahlfors $d$-regular set $E$ in $\mathbb{R}^{n}$ is uniformly rectifiable if the set of pairs $(x,r)\in E\times (0,\infty)$ for which there exists $y \in B(x,r)$ and $0<t<r$ satisfying $\mathscr{H}^{d}_{\infty}(E\cap…

We consider a special class of weak dependent random variables with control on covariances of Lipschitz transformations. This class includes, but is not limited to, positively, negatively associated variables and a few other classes of…