论文标题
Green的二阶抛物线方程的功能具有单数较低阶系系数
Green's function for second order parabolic equations with singular lower order coefficients
论文作者
论文摘要
我们构建格林的功能，以构建形式的二阶抛物面操作员$ pu = \ partial_t u- {\ rm div}（{{\ bf a} \ nabla u++ boldsymbol {b} u {b} u）+ \ boldsymbol是$ \ mathbb {r}^n $中的开放连接集。不必将$ω$限制为$ω$，$ω= \ mathbb {r}^n $不排除在外。我们假设领先的系数$ \ bf a $是有界和可测量的，较低阶系系数$ \ boldsymbol {b} $，$ \ boldsymbol {c} $，$ d $属于关键的混合混合混合的norm lebesgue lebesgue lebesgue lebesgue lebesgue lebesgue空间，并满足条件$ d- {\ rm div} $ div} \ ge boldsymbol＆ge bolbol { div}（\ boldsymbol {b} - \ boldsymbol {c}）\ ge 0 $。我们表明，绿色的功能在整个$（ - \ infty，\ infty）\ timesω$中具有高斯绑定。
We construct Green's functions for second order parabolic operators of the form $Pu=\partial_t u-{\rm div}({\bf A} \nabla u+ \boldsymbol{b}u)+ \boldsymbol{c} \cdot \nabla u+du$ in $(-\infty, \infty) \times Ω$, where $Ω$ is an open connected set in $\mathbb{R}^n$. It is not necessary that $Ω$ to be bounded and $Ω= \mathbb{R}^n$ is not excluded. We assume that the leading coefficients $\bf A$ are bounded and measurable and the lower order coefficients $\boldsymbol{b}$, $\boldsymbol{c}$, and $d$ belong to critical mixed norm Lebesgue spaces and satisfy the conditions $d-{\rm div} \boldsymbol{b} \ge 0$ and ${\rm div}(\boldsymbol{b}-\boldsymbol{c}) \ge 0$. We show that the Green's function has the Gaussian bound in the entire $(-\infty, \infty) \times Ω$.
