Interpolating estimates with applications to some quantitative symmetry results

Rolando Magnanini, Giorgio Poggesi

Research output: Contribution to journalArticlepeer-review

7 Citations (Scopus)

Abstract

We prove interpolating estimates providing a bound for the oscillation of a function in terms of two Lp norms of its gradient. They are based on a pointwise bound of a function on cones in terms of the Riesz potential of its gradient. The estimates hold for a general class of domains, including, e.g., Lipschitz domains. All the constants involved can be explicitly computed. As an application, we show how to use these estimates to obtain stability for Alexandrov's Soap Bubble Theorem and Serrin's overdetermined boundary value problem. The new approach results in several novelties and benefits for these problems.
Original languageEnglish
JournalMathematics In Engineering
Volume5
Issue number1
Early online date10 Jan 2022
DOIs
Publication statusPublished - 2023

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