论文标题
Lipschitz域中具有非常奇异电位的Schrodinger方程
Schrodinger equations with very singular potentials in Lipschitz domains
论文作者
论文摘要
考虑操作员$ l^{v}：=δ+ v $在有限的Lipschitz域中$ω\ subset \ Mathbb {r}^n $。假设$ v \ in c^{1,1}（ω）$和$ v $满足$ v（x）\ leq \ leq \ overline {a} \ mathrm {dist}（x，x，x，\partialΩ）例如，如果$ v> 0 $此条件读取$ 1 <c_h（v）$（=相对于$ v $的harty常数）。我们得出估计值$ l_v $谐波功能和{\ Mathfrak M} _+（ω;φ_v）$中的度量$τ\的正绿色电位的估计值。这些暗示估计为正$ l_v $ supersolutions和$ l_v $ subsolutions。在平滑域的情况下，在[7]中也获得了类似的结果。
Consider operators $L^{V}:=Δ+ V$ in a bounded Lipschitz domain $Ω\subset \mathbb{R}^N$. Assume that $V\in C^{1,1}(Ω)$ and $V$ satisfies $V(x) \leq \overline{a} \mathrm{dist}(x,\partialΩ)^{-2}$ in $Ω$ and a second condition that guarantees the existence of a ground state $Φ_V$. If, for example, $V>0$ this condition reads $1<c_H(V)$ (= the Hardy constant relative to $V$). We derive estimates of positive $L_V$ harmonic functions and of positive Green potentials of measures $τ\in {\mathfrak M}_+(Ω;Φ_V)$. These imply estimates of positive $L_V$ supersolutions and of $L_V$ subsolutions. Similar results have been obtained in [7] in the case of smooth domains.
