July 15, 2024Open Access

Fourth-order operators with unbounded coefficients in L¹ spaces

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Abstract

We prove that operators of the form A=-a (x) ²^2, 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) ^ ^2, 02. Moreover, we characterise the maximal domain of A in L¹ (RN).

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Gregorio et al. (Mon,) studied this question.

synapsesocial.com/papers/68e60550b6db64358759894f https://doi.org/https://doi.org/10.48550/arxiv.2407.10551

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