Sums of linear operators of parabolic type: a priori estimates and strong solutions |
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Authors: | Marco Fuhrman |
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Institution: | (1) Present address: Dipartimento di Matematica, Politecnico di Milano, via Bonardi 9, 20133 Milano, Italy |
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Abstract: | Summary We study the equation (A – ) x + (B– )x=y, with unknown x, in a Banach space X. y Xis the datum, > 0, A and B are linear closed unbounded operators in X with domains DA, DB. In the non commutative case, under assumptions already considered in the literature (see 7]), we show that for large values of any solution x DA DB satisfies an a priori estimate ¦|x¦| c –1¦|y||and we prove that for any y X there exists a unique strong solution x, i.e. there exist xn DA DB such that xn x, (A– ) xn+(B– ) xn y in X. We also study regularity properties of strong solutions and we show that they belong to suitable interpolation spaces between DA (or DB) and X. |
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