ﻻ يوجد ملخص باللغة العربية
We show that, if $bin L^1(0,T;L^1_{mathrm{loc}}(mathbb{R}))$ has spatial derivative in the John-Nirenberg space $mathrm{BMO}(mathbb{R})$, then it generalizes a unique flow $phi(t,cdot)$ which has an $A_infty(mathbb R)$ density for each time $tin [0,T]$. Our condition on the map $b$ is optimal and we also get a sharp quantitative estimate for the density. As a natural application we establish a well-posedness for the Cauchy problem of the transport equation in $mathrm{BMO}(mathbb R)$.
Let $p(cdot): mathbb R^nto(0,infty)$ be a variable exponent function satisfying the globally log-Holder continuous condition. In this article, the authors first obtain a decomposition for any distribution of the variable weak Hardy space into good an
Closed form expressions are proposed for the Feynman integral $$ I_{D, m}(p,q) = intfrac{d^my}{(2pi)^m}intfrac{d^Dx}{(2pi)^D} frac1{(x-p/2)^2+(y-q/2)^4} frac1{(x+p/2)^2+(y+q/2)^4} $$ over $d=D+m$ dimensional space with $(x,y),,(p,q)in mathb
Wild sets in $mathbb{R}^n$ can be tamed through the use of various representations though sometimes this taming removes features considered important. Finding the wildest sets for which it is still true that the representations faithfully inform us a
In this paper, we prove two improv
Let $p(cdot): mathbb R^nto(0,1]$ be a variable exponent function satisfying the globally log-Holder continuous condition and $L$ a one to one operator of type $omega$ in $L^2({mathbb R}^n)$, with $omegain[0,,pi/2)$, which has a bounded holomorphic fu