We consider a class of vector-valued elliptic operators with unbounded coefficients, coupled up to the first order, in the Lebesgue space Lp(Rd; Rm) with p∈ (1 , ∞). Sufficient conditions to prove generation results of an analytic C-semigroup T(t) , together with a characterization of the domain of its generator, are given. Some results related to the hypercontractivity and the ultraboundedness of the semigroup are also established.
Generation results for vector-valued elliptic operators with unbounded coefficients in Lp spaces / Angiuli, L.; Lorenzi, L.; Mangino, E. M.; Rhandi, A.. - In: ANNALI DI MATEMATICA PURA ED APPLICATA. - ISSN 0373-3114. - 201:(2022), pp. 1347-1379. [10.1007/s10231-021-01160-z]
Generation results for vector-valued elliptic operators with unbounded coefficients in Lp spaces
Angiuli L.
;Lorenzi L.;Rhandi A.
2022-01-01
Abstract
We consider a class of vector-valued elliptic operators with unbounded coefficients, coupled up to the first order, in the Lebesgue space Lp(Rd; Rm) with p∈ (1 , ∞). Sufficient conditions to prove generation results of an analytic C-semigroup T(t) , together with a characterization of the domain of its generator, are given. Some results related to the hypercontractivity and the ultraboundedness of the semigroup are also established.I documenti in IRIS sono protetti da copyright e tutti i diritti sono riservati, salvo diversa indicazione.
