Related papers: Towards sharp Bohnenblust--Hille constants

This work addresses the problem of (global) maximal regularity for quasilinear evolution equations with sublinear gradient growth and right-hand side in Lebesgue spaces, complemented with Neumann boundary conditions. The proof relies on a…

In this paper we study sharp pointwise inequalities for maximal operators. In particular, we strengthen DeVore's inequality for the moduli of smoothness and a logarithmic variant of Bennett--DeVore--Sharpley's inequality for rearrangements.…

In this paper, we consider functionals based on moments and non-linear entropies which have a linear growth in time in case of source-type so-lutions to the fast diffusion or porous medium equations, that are also known as Barenblatt…

We show that the use of suitable theorems for black hole formation in Friedmann expanding universes leads to a modification of the Bekenstein-Hawking entropy. By adopting an argument similar to the original Bekenstein one, we write down the…

Morrey's classical inequality implies the H\"older continuity of a function whose gradient is sufficiently integrable. Another consequence is the Hardy-type inequality $$ \lambda\biggl\|\frac{u}{d_\Omega^{1-n/p}}\biggr\|_{\infty}^p\le…

If we interpret the Bekenstein-Hawking entropy of the Hubble horizon as thermodynamic entropy, then the entanglement entropy of the superhorizon modes of curvature perturbation entangled with the subhorizon modes will exceed the…

In this work, we summarize the linearization method to study the Heisenberg Uncertainty Principles, and explain that the same approach can be used to handle the stability problem. As examples of application, combining with spherical…

We examine the classic problem of homogeneous nucleation and growth by deriving and analyzing a fully discrete stochastic master equation. Upon comparison with results obtained from the corresponding mean-field Becker-D\"{o}ring equations…

For a given irrational number $\alpha$ and a real number $\gamma$ in $(0,1)$ one defines the two-sided inhomogeneous approximation constant \begin{equation*} M(\alpha,\gamma):=\liminf_{|n|\rightarrow\infty}|n| ||n\alpha-\gamma||,…

We point out that, due to the nonlinearity of the Einstein equations, a homogeneous approximation in cosmology leads to the appearance of an additional term in the Friedmann equation. This new term is associated with the spatial…

We study the sharp constant in the Morrey inequality for fractional Sobolev-Slobodecki\u{\i} spaces on the whole $\mathbb{R}^N$. By generalizing a recent work by Hynd and Seuffert, we prove existence of extremals, together with some…

Higher order derivative corrections to the Einstein--Maxwell action are considered and an explicit form is found for the corrections to the entropy of extremal black holes. We speculate on the properties of these corrections from the point…

In this article we establish new improvements of the optimal Hardy inequality in the half space. We first add all possible linear combinations of Hardy type terms thus revealing the structure of this type of inequalities and obtaining best…

This paper studies the Hardy-type inequalities on the discrete intervals. The first result is the variational formulas of the optimal constants. Using these formulas, one may obtain an approximating procedure and the known basic estimates…

The study of the optimal constant in an Hessian-type Sobolev inequality leads to a fully nonlinear boundary value problem, overdetermined with non standard boundary conditions. We show that all the solutions have ellipsoidal symmetry. In…

We revisit the classical theory of linear second-order uniformly elliptic equations in divergence form whose solutions have H\"older continuous gradients, and prove versions of the generalized maximum principle, the $C^{1,\alpha}$-estimate,…

In this paper, we prove the anisotropic Shannon inequality for the Renyi entropy with the best constant on Folland-Stein homogeneous Lie groups. As a consequence, we also prove the optimal Shannon inequality in the same setting. Using a…

The Hardy--Littlewood inequality for complex homogeneous polynomials asserts that given positive integers $m\geq2$ and $n\geq1$, if $P$ is a complex homogeneous polynomial of degree $m$ on $\ell_{p}^{n}$ with $2m\leq p\leq\infty$ given by…

As a compelling pattern for the holographic principle, our covariant entropy bound conjecture is proposed for more general dynamical horizons. Then we apply our conjecture to $\Lambda$CDM cosmological models, where we find it imposes a…

Various lower bounds are established for the entropy of sums, products and their combinations. First, we derive a prime-field analogue of a version of the entropy power inequality established by Tao over torsion-free groups. Next, we prove…