Analytic semigroups generated in \(L^p\) by elliptic operators with high order degeneracy at the boundary (Q2902314)

Let \(\Omega\) be a bounded open subset of \({\mathbb R}^{N+1}\) with \(C^2\) boundary. In 1989, \textit{V. Vespri} [Ann. Mat. Pura Appl., IV. Ser. 155, 353--388 (1989; Zbl 0709.35065)] proved, among other things, that an elliptic operator whose diffusion coefficients degenerate at the boundary at least as the square of the distance from boundary, with a suitable domain, generates an analytic semigroup in \(L^p(\Omega)\) (\(1<p<\infty\)). In this paper, the authors give a new and different proof of this result based on their previous work.