On the multiple membranes problem
classification
🧮 math.AP
keywords
blow-upmembranesmultipleproblemanalysisboundaryclassificationcomplete
read the original abstract
We establish the optimal regularity for solutions to the multiple membranes problem, and perform a blow-up analysis at points on the free boundary with the highest multiplicity. This leads to a complete classification of blow-up profiles in the plane. The main technical tool is a Weiss-type monotonicity formula.
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