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Real-valued valuations on Sobolev spaces

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Abstract

Continuous, SL(n) and translation invariant real-valued valuations on Sobolev spaces are classified. The centro-affine Hadwiger’s theorem is applied. In the homogeneous case, these valuations turn out to be L p-norms raised to p-th power (up to suitable multipication scales).

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  1. Institut für Diskrete Mathematik und Geometrie, Technische Universität Wien, Wien, 1040, Austria

    Dan Ma

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  1. Dan Ma
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Ma, D. Real-valued valuations on Sobolev spaces. Sci. China Math. 59, 921–934 (2016). https://doi.org/10.1007/s11425-015-5101-6

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  • DOI: https://doi.org/10.1007/s11425-015-5101-6

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