On a class of elliptic operators with unbounded diffusion coefficients
Giorgio Metafune, Chiara Spina, Cristian Tacelli · Evolution equations and control theory · 2014
We prove that, for $-\infty <\alpha\leq 2$, $1 < p <\infty$,the operator $L = (1+|x|^2)^\frac{\alpha}{2}\sum_{i,j=1}^N a_{ij}(x)D_{ij}$ generates an analyticsemigroup in $L^p(\mathbb{R}^N)$ when the diffusion coefficients $a_{ij}$ admit a limit at infinity.