Abstract
We consider the operator
with \(\alpha >2\), \(0<\alpha -N<\beta \le \alpha -2\), \(b\ge \frac{\alpha (N-2+\alpha )}{p}\), \(c>0\) and \(N\ge 3\). Under suitable assumptions, we show that the maximal realization \(L_{p,max}\) of L with a suitable domain generates a contraction \(C_{0}\)-semigroup in \(L^{p}(\mathbb {R}^{N})\), \(1<p<\infty \), which is analytic if \(p>\frac{N}{N-2}\).
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Metoui, I. Generation of analytic semigroups by elliptic operators with unbounded diffusion, drift and potential terms. J Elliptic Parabol Equ 10, 547–557 (2024). https://doi.org/10.1007/s41808-024-00273-9
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DOI: https://doi.org/10.1007/s41808-024-00273-9