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. - (2021). [10.1007/s10231-021-01160-z]
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