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Steiner Symmetrization is Continuous in W1,p

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Abstract.

We study the continuity, smoothing, and convergence properties of Steiner symmetrization in higher space dimensions. Our main result is that Steiner symmetrization is continuous in W 1, p \( (1 \leq p < \infty) \) in all dimensions. This implies that spherical symmetrization cannot be approximated in W 1, p by sequences of Steiner symmetrizations. We also give a quantitative version of the standard energy inequalities for spherical symmetrization.

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  1. Almut Burchard, Department of Mathematics, Princeton University, Princeton, NJ 08544, USA, e-mail: burchard@math.princeton.edu, , , , , , US

    A. Burchard

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  1. A. Burchard
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Submitted: September 1996

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Burchard, A. Steiner Symmetrization is Continuous in W1,p. GAFA, Geom. funct. anal. 7, 823–860 (1997). https://doi.org/10.1007/s000390050027

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  • DOI: https://doi.org/10.1007/s000390050027

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