We study stability issues for some integral inequalities, in particular for the extremal case of the so-called Borell–Brascamp–Lieb inequalities. In this case, when near equality is realized in dimension one, we prove that the involved functions must be (Formula presented.)-close to be quasiconcave. Further results about equality conditions in some other cases are provided.
Stability for a strengthened Borell–Brascamp–Lieb inequality / Rossi, Andrea*; Salani, Paolo. - In: APPLICABLE ANALYSIS. - ISSN 0003-6811. - STAMPA. - 98:(2019), pp. 1773-1784. [10.1080/00036811.2018.1451645]
Stability for a strengthened Borell–Brascamp–Lieb inequality
Rossi, Andrea;Salani, Paolo
2019
Abstract
We study stability issues for some integral inequalities, in particular for the extremal case of the so-called Borell–Brascamp–Lieb inequalities. In this case, when near equality is realized in dimension one, we prove that the involved functions must be (Formula presented.)-close to be quasiconcave. Further results about equality conditions in some other cases are provided.
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