论文标题
Schrödinger经营者的Green内核和Martin Kernel具有奇异的潜力，并适用于B.V.P.对于线性椭圆方程
Green kernel and Martin kernel of Schrödinger operators with singular potential and application to the B.V.P. for linear elliptic equations
论文作者
论文摘要
令$ c^2 $有界域，$ c^2 $有界域和$ k \ subsetω$是紧凑的，$ c^2 $ submanifold in $ \ mathbb {r}^n $，$ c^2 $ submanifold，$ c^2;我们考虑schrödinger运算符$l_μ=δ+μd_k^{ - 2} $ in $ω\ setMinus k $，其中$ d_k（x）= \ text {dist {dist}（x，k）$。最佳的Hardy常数$ H =（N-K-2）/2 $深度参与了$-L_μ$的研究。当$μ\ leq h^2 $时，我们为$-L_μ$的绿色内核和Martin内核建立了尖锐的双面估计。我们使用这些估计来证明边界价值问题解决方案的存在，独特性和先验估计，并通过与$-L_μ$相关的线性方程式进行测量。
Let $Ω\subset \mathbb{R}^N$ ($N \geq 3$) be a $C^2$ bounded domain and $K \subset Ω$ be a compact, $C^2$ submanifold in $\mathbb{R}^N$ without boundary, of dimension $k$ with $0\leq k < N-2$. We consider the Schrödinger operator $L_μ= Δ+ μd_K^{-2}$ in $Ω\setminus K$, where $d_K(x) = \text{dist}(x,K)$. The optimal Hardy constant $H=(N-k-2)/2$ is deeply involved in the study of $-L_μ$. When $μ\leq H^2$, we establish sharp, two-sided estimates for Green kernel and Martin kernel of $-L_μ$. We use these estimates to prove the existence, uniqueness and a priori estimates of the solution to the boundary value problem with measures for linear equations associated to $-L_μ$
