We prove that the realization A_p in Lp(R^N), 1 < p < infty , of the elliptic operator A = (1+|x|^alpha)Delta +b|x|^{alpha -2}x abla -c|x|^eta with domain D(Ap) = {u in W^{2,p}(R^N) : Au in Lp(RN)} generates a strongly continuous analytic semigroup T(t) provided that alpha > 2, eta > alpha - 2 and any constants b in R and c > 0. This generalizes recent results in in the litterature. Moreover we show that T(t) is consistent, immediately compact and ultracontractive.
Elliptic operators with unbounded diffusion, drift and potential terms
Gregorio, Federica;RHANDI, Abdelaziz
;Tacelli, Cristian
2018
Abstract
We prove that the realization A_p in Lp(R^N), 1 < p < infty , of the elliptic operator A = (1+|x|^alpha)Delta +b|x|^{alpha -2}x abla -c|x|^eta with domain D(Ap) = {u in W^{2,p}(R^N) : Au in Lp(RN)} generates a strongly continuous analytic semigroup T(t) provided that alpha > 2, eta > alpha - 2 and any constants b in R and c > 0. This generalizes recent results in in the litterature. Moreover we show that T(t) is consistent, immediately compact and ultracontractive.File in questo prodotto:
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