A homogeneity improvement approach to the obstacle problem |
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| Authors: | Georg S. Weiss |
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| Affiliation: | (1) Department of Mathematics, Faculty of Science, Tokyo Institute of Technology, O-okayama 2-12-1, Tokyo, 152 Japan (e-mail: gw@math.titech.ac.jp), JP |
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| 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. Oblatum 20-IV-1998 & 12-II-1999 / Published online: 21 May 1999 |
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