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L∞-Estimates for the Torsion Function and L∞-Growth of Semigroups Satisfying Gaussian Bounds

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Abstract

We investigate selfadjoint C0-semigroups on Euclidean domains satisfying Gaussian upper bounds. Major examples are semigroups generated by second order uniformly elliptic operators with Kato potentials and magnetic fields. We study the long time behaviour of the L∞ operator norm of the semigroup. As an application we prove a new L∞-bound for the torsion function of a Euclidean domain that is close to optimal.

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Acknowledgments

The author would like to thank Michiel van den Berg for the introduction to the topic and for helpful discussions.

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Authors and Affiliations

  1. Fachbereich 3 – Mathematik, Universität Bremen, 28359, Bremen, Germany

    Hendrik Vogt

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  1. Hendrik Vogt
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Vogt, H. L∞-Estimates for the Torsion Function and L∞-Growth of Semigroups Satisfying Gaussian Bounds. Potential Anal 51, 37–47 (2019). https://doi.org/10.1007/s11118-018-9701-y

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  • DOI: https://doi.org/10.1007/s11118-018-9701-y

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