We prove that the realization A_p in L^p(R^N) of the Schroedinger type operator A=(1+|x|^{alpha})Delta-|x|^{beta} with domain D(A_p)={u in W^{2,p}(R^N): Au in L^p(R^N)} generates a strongly continuous analytic semigroup provided that N>2, alpha >2 and beta >alpha -2. Moreover this semigroup is consistent, irreducible, immediately compact and ultracontractive.
Schrodinger type operators with unbounded diffusion and potential terms
CANALE, Anna;RHANDI, Abdelaziz
;TACELLI, CRISTIAN
2016
Abstract
We prove that the realization A_p in L^p(R^N) of the Schroedinger type operator A=(1+|x|^{alpha})Delta-|x|^{beta} with domain D(A_p)={u in W^{2,p}(R^N): Au in L^p(R^N)} generates a strongly continuous analytic semigroup provided that N>2, alpha >2 and beta >alpha -2. Moreover this semigroup is consistent, irreducible, immediately compact and ultracontractive.File in questo prodotto:
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A.Canale-C.Tacelli-A.Rhandi, Schrodinger-type operator for Vqr.pdf
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