We prove that operators of the form A=-a(x)(2)Delta (2), with |Da(x)| <= ca(x) (1/2), generate analytic semigroups in L-p(R-N) for 1 < p <= infinity and in C-b(R-N). In particular, we deduce generation results for the operator A := -(1 + |x|(2))(alpha) Delta (2), 0 <= alpha <= 2. Moreover, we characterize the maximal domain of such operators in L-p(R-N) for 1 < p < infinity.
FOURTH-ORDER OPERATORS WITH UNBOUNDED COEFFICIENTS
Spina C.;Tacelli C.
2024-01-01
Abstract
We prove that operators of the form A=-a(x)(2)Delta (2), with |Da(x)| <= ca(x) (1/2), generate analytic semigroups in L-p(R-N) for 1 < p <= infinity and in C-b(R-N). In particular, we deduce generation results for the operator A := -(1 + |x|(2))(alpha) Delta (2), 0 <= alpha <= 2. Moreover, we characterize the maximal domain of such operators in L-p(R-N) for 1 < p < infinity.File in questo prodotto:
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