On regularity and singularity of free boundaries in obstacle problems

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.

Keywords

Free boundary / Monotonicity / Dimension reduction / Uniqueness of blow-ups

References

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