Green kernel and Martin kernel of Schr\"odinger operators with singular potential and application to the B.V.P. for linear elliptic equations

25 Feb 2020 Gkikas Konstantinos T. Nguyen Phuoc-Tai

Let $\Omega \subset \mathbb{R}^N$ ($N \geq 3$) be a $C^2$ bounded domain and $K \subset \Omega$ be a compact, $C^2$ submanifold in $\mathbb{R}^N$ without boundary, of dimension $k$ with $0\leq k < N-2$. We consider the Schr\"odinger operator $L_\mu = \Delta + \mu d_K^{-2}$ in $\Omega \setminus K$, where $d_K(x) = \text{dist}(x,K)$... (read more)

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