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On regularity and singularity of free boundaries in obstacle problems

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Abstract

The author presents a simple approach to both regularity and singularity theorems for free boundaries in classical obstacle problems. This approach is based on the monotonicity of several variational integrals, the Federer-Almgren dimension reduction and stratification theorems, and some simple PDE arguments.

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Authors and Affiliations

  1. Courant Institute of Mathematical Sciences, New York University, 251 Mercer Street, New York, 10012, USA

    Fanghua Lin

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  1. Fanghua Lin
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Correspondence to Fanghua Lin.

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Dedicated to Professor Andrew Majda on the Occasion of his 60th Birthday

Project supported by the National Science Foundation (No. DMS 0700517).

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Lin, F. On regularity and singularity of free boundaries in obstacle problems. Chin. Ann. Math. Ser. B 30, 645–652 (2009). https://doi.org/10.1007/s11401-009-0174-6

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  • DOI: https://doi.org/10.1007/s11401-009-0174-6

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