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.
2021-01-01
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.File in questo prodotto:
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