论文标题
内饰Schauder对与Lévy操作员相关的椭圆方程的估算
Interior Schauder estimates for elliptic equations associated with Lévy operators
论文作者
论文摘要
我们研究了对integro-differention方程的本地解决方案$ f $ $ f $ $$ af = g \ quad \ text {in $ u $} $} $} $} $ a $ a $ a $ a $ a $ a $ a $ a $ a $ a $ a $ a $（x_t）_ {t \ geq 0} $。假设$（x_t）_ {t \ geq 0} $的过渡密度满足一定的梯度估计值，我们建立了对点和弱解决方案$ f $的内部schauder估计。我们的结果适用于广泛的Lévy发电机，包括稳定的Lévy工艺和次级布朗动作的发电机。
We study the local regularity of solutions $f$ to the integro-differential equation $$ Af=g \quad \text{in $U$}$$ associated with the infinitesimal generator $A$ of a Lévy process $(X_t)_{t \geq 0}$. Under the assumption that the transition density of $(X_t)_{t \geq 0}$ satisfies a certain gradient estimate, we establish interior Schauder estimates for both pointwise and weak solutions $f$. Our results apply for a wide class of Lévy generators, including generators of stable Lévy processes and subordinated Brownian motions.
