We prove that operators of the form A=-a(x)²Δ², with suitable growth conditions on the coefficient $a(x)$, generate analytic semigroups in L¹(RN). In particular, we deduce generation results for the operator A :=- (1+|x|²)α Δ², 0≤α≤2. Moreover, we characterise the maximal domain of A in L¹(RN).
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Gregorio et al. (2024) studied this question.
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