论文标题
奇异性的年轻方程
Young equations with singularities
论文作者
论文摘要
在本文中，我们证明了对年轻方程式$ dy（t）= ay（t）dt+σ（y（t））dx（t）$，$ t \ in [0，t] $，$ y（$ y（0）=ψ$）的存在和独特性。在这里，$ a $是一个无限的运算符，在Banach Space $ X $上，生成有界线性运算符$（s（t））_ {t \ geq 0} $的半元组，$ x $，$ x $是真实价值的$η$ -H $-Hölder连续。我们的目的是减少参考书目中的[4]和[1]和[1]（另请参见[2,5]），最初的基准$ψ$的规律性要求最终将其丢弃。 主要工具是针对新的增量的缝纫地图的定义，该缝纫地图允许在一般间隔$ [a，b] \ subset \ mathbb r $中构建年轻的卷积积分，当该功能下的$x_α$ - $x_α$ norm the Integral sign blass blass bloved接近$ a $ a $ a $和$x_α$是$x_α$是$ x $ x $ x $ x $和$ x $ d（a a a）之间的$x_α$。
In this paper we prove existence and uniqueness of a mild solution to the Young equation $dy(t)=Ay(t)dt+σ(y(t))dx(t)$, $t\in[0,T]$, $y(0)=ψ$. Here, $A$ is an unbounded operator which generates a semigroup of bounded linear operators $(S(t))_{t\geq 0}$ on a Banach space $X$, $x$ is a real-valued $η$-Hölder continuous. Our aim is to reduce, in comparison to [4] and [1] (see also [2,5]) in the bibliography, the regularity requirement on the initial datum $ψ$ eventually dropping it. The main tool is the definition of a sewing map for a new class of increments which allows the construction of a Young convolution integral in a general interval $[a,b]\subset \mathbb R$ when the $X_α$-norm of the function under the integral sign blows up approaching $a$ and $X_α$ is an intermediate space between $X$ and $D(A)$.
