3:00 pm Friday, April 6, 2018
Junior Analysis: The Mean Value Theorem for Elliptic Operators in Divergence Form by Maria Soria in 11.176
It is well known that harmonic functions satisfy the mean value property, that is, the value of the function at a point equals its average on any ball centered at the point and compactly contained in the domain of definition. Thanks to this property, we can show many important results such as the maximum principle, Harnack inequality, interior regularity... In this talk, we will see that elliptic operators in divergence form also satisfy such a nice property, where the mean value sets are comparable to balls. This was first stated by L. Caffarelli, in the Fermi lectures in 1998, and then, it was proved rigorously by I. Blank and Z. Hao in 2014. Submitted by
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