Dr. Ashok Aryal will present his research at Prairie Analysis Seminar (PAS Conference) taking place at Kansas State University this Friday and Saturday, Sept. 8-9. The title of his talk is “Density of the zero set for a generalized Bernoulli-type free boundary problem.”
Abstract of the talk: In a famous paper in 1980, Alt and Caffarelli showed existence and regularity for a Bernoulli type free boundary arising in a number of applications including flow problems. One notable property of the problem is that the zero set and the positivity set both have positive density at the free boundary, and so the free boundary cannot have cusps in either direction. Very recently, dos Prazeres and Teixeira studied the same problem but for arbitrary uniformly elliptic divergence form operators and they proved that the positivity set has positive density. Applying the generalized mean value theorem, proven by Blank and Hao for arbitrary uniformly elliptic divergence form operators, we have been able to prove that the zero set of this type of FBP has also positive density. In this talk I will introduce the Bernoulli type FBP and present my result.