论文标题
椭圆形和抛物线方程解决方案的渐近行为，其无界域的无界系数无界域
Asymptotic behavior of solutions to elliptic and parabolic equations with unbounded coefficients of the second orderin unbounded domains
论文作者
论文摘要
我们研究了在二维外部结构域中对第二阶的椭圆方程解决方案的渐近行为。在假设该解决方案属于$ l^q $，而[2，\ infty）$中的$ q \ $ q \，我们证明，就系数的行为而言，在空间无穷大的解决方案的渐近估算值。作为推论，我们获得了liouville型定理，如果系数可能在空间无穷大处生长。我们还研究了$ n $维的整个空间中的相应抛物线问题，并讨论了$ l^q $的解决方案的能源身份。作为推论，我们还展示了前进和古代解决方案的liouville型定理。
We study an asymptotic behavior of solutions to elliptic equations of the second order in a two dimensional exterior domain. Under the assumption that the solution belongs to $L^q$ with $q \in [2,\infty)$, we prove a pointwise asymptotic estimate of the solution at the spatial infinity in terms of the behavior of the coefficients. As a corollary, we obtain the Liouville-type theorem in the case when the coefficients may grow at the spacial infinity. We also study a corresponding parabolic problem in the $n$-dimensional whole space and discuss the energy identity for solutions in $L^q$. As a corollary we show also the Liouville-type theorem for both forward and ancient solutions.
