论文标题
$ l^2（\ Mathbb {r}^n）$的第四阶Schrödinger类型运算符带有未绑定系数的运算符
Fourth-order Schrödinger type operator with unbounded coefficients in $L^2(\mathbb{R}^N)$
论文作者
论文摘要
在本文中，我们研究生成会导致$ l^2（\ mathbb {r}^n）$对于第四阶Schrödinger类型运算符，其$$ a = a = a = a^{2}Δ^{2}Δ^^2+v^{2+v^{2} $ a（ $β>（α-2）^+$。我们获得该$（-a，d（a））$在$ l^2（\ Mathbb {r}^n）$中以$ n \ geq5 $生成一个分析性的连续分析。此外，最大域$ d（a）$可以用加权Sobolev空间以$ n> 8 $的特征来表征 \ [d_2（a）= \ { l^{2}（\ mathbb {r}^n）\ text {for} h = 0,1,1,2,3,4 \}。 \]
In this paper we study generation results in $L^2(\mathbb{R}^N)$ for the fourth order Schrödinger type operator with unbounded coefficients of the form $$A=a^{2} Δ^2+V^{2}$$ where $a(x)=1+|x|^α$ and $V=|x|^β$ with $α>0$ and $β>(α-2)^+$. We obtain that $(-A,D(A))$ generates an analytic strongly continuous semigroup in $L^2(\mathbb{R}^N)$ for $N\geq5$. Moreover, the maximal domain $D(A)$ can be characterized for $N>8$ by the weighted Sobolev space \[ D_2(A)=\{u\in H^{4}(\mathbb{R}^N)\,:\,V^{2}u\in L^{2}(\mathbb{R}^N), |x|^{2α-h}D^{4-h}u\in L^{2}(\mathbb{R}^N) \text{ for } h=0,1,2,3,4\}. \]
