In this paper we study minimal realizations in Lp(RN) of the second order elliptic operator Ab,c:=(1+|x|α)Δ+b|x|α−2x⋅∇−c|x|α−2−|x|β,x∈RN, where N≥3, α∈[0,2), β>0, and b,c are real numbers. We use quadratic form methods to prove that (Ab,c,Cc∞(RN∖{0})) admits an extension that generates an analytic C0-semigroup for all p∈(1,∞). Moreover, we give conditions on the coefficients under which this extension is precisely the closure of (Ab,c,Cc∞(RN∖{0})).
Some results on second-order elliptic operators with polynomially growing coefficients in Lp-spaces
Caso L.;Gregorio F.
;Tacelli C.
2021-01-01
Abstract
In this paper we study minimal realizations in Lp(RN) of the second order elliptic operator Ab,c:=(1+|x|α)Δ+b|x|α−2x⋅∇−c|x|α−2−|x|β,x∈RN, where N≥3, α∈[0,2), β>0, and b,c are real numbers. We use quadratic form methods to prove that (Ab,c,Cc∞(RN∖{0})) admits an extension that generates an analytic C0-semigroup for all p∈(1,∞). Moreover, we give conditions on the coefficients under which this extension is precisely the closure of (Ab,c,Cc∞(RN∖{0})).File in questo prodotto:
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