Abstract.
This paper contains a new approach to regularity and singularity of the obstacle problem: by means of an epiperimetric inequality and a monotonicity formula an energy decay estimate is derived. As a consequence, the increase in the solution’s homogeneity when passing to a smaller ball can be estimated. This leads to uniqueness of blow-up limits and regularity in that order.
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Oblatum 20-IV-1998 & 12-II-1999 / Published online: 21 May 1999
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Weiss, G. A homogeneity improvement approach to the obstacle problem. Invent. math. 138, 23–50 (1999). https://doi.org/10.1007/s002220050340
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DOI: https://doi.org/10.1007/s002220050340