A degenerate elliptic operator with unbounded diffusion coefficients (Q2509472)

Summary: We prove that, for \(N \geq 3\), the operator \(L=|x|^\alpha\Delta\) generates an analytic semigroup in \(L^{p}(\mathbb R^N)\) if \(\alpha=2\) and \(1<p<\infty\) or \(\alpha<2\) and \(\frac{N}{N-\alpha}< p<\infty\) or \(\alpha> 2\) and \(\frac{N}{N-2}<p<\infty\). The above bounds are shown to be sharp.