A doubly monotone flow for constant width bodies in $\mathbb{R}^3$

On the operator Aczél inequality and its reverse

In this paper, we present some operator and eigenvalue inequalities involving operator monotone, doubly concave and doubly convex functions. These inequalities provide some variants of operator Aczél inequality and its reverse via generalized Kantorovich constant.

Monotone substochastic operators and a new Calderon couple

An important result on submajorization, which goes back to Hardy, Littlewood and Pólya, states that $b\preceq a$ if and only if there is a doubly stochastic matrix $A$ such that $b=Aa$. We prove that under monotonicity assumptions on vectors $a$ and $b$ respective matrix $A$ may be chosen monotone. This result is then applied to show that $(\widetilde{L^p},L^{\infty})$ is a Calderón couple for $1\leq p<\infty $, where $\widetilde{L^{p}}$ is the Köthe dual of the Cesàro space $Ces_{p'}$ (or equivalently the down space $L^{p'}_{\downarrow}$). In particular, $(\widetilde{L^1},L^{\infty})$ is a Ca…

关于Musielak-Orlicz空间中一类双非线性演化方程

On a class of doubly nonlinear evolution equations in Musielak-Orlicz spaces

本文在Musielak-Orlicz空间中研究一类双非线性演化方程，通过建立次微分算子理论及极大单调算子逼近框架，证明了一大类算子的弱解存在性，并给出多个应用实例。

非自反Banach空间中具有退化耗散势的Orlicz型函数空间与广义梯度流：理论与应用

Orlicz-type Function Spaces and Generalized Gradient Flows with Degenerate Dissipation Potentials in Non-Reflexive Banach Spaces: Theory and Application

本论文研究非自反Banach空间中广义梯度流强解存在性与Banach值Orlicz空间理论，拓展对偶理论并改进已有结果，结合二者为任意增长率的微分方程分析提供工具，且通过Allen-Cahn-Gurtin型问题弱解存在性验证其有效性。