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Analysis
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Mary Vaughan , PMA 10.176: Harnack inequality for fractional elliptic equations in nondivergence form
Wednesday, December 01, 2021, 01:00pm - 02:00pm
In this talk, we will define fractional powers of nondivergence form elliptic operators in bounded domains under minimal regularity assumptions and highlight several applications. We will characterize a Poisson problem driven by such operators with a degenerate/singular extension problem. We then develop the method of sliding paraboloids in the Monge-Ampère geometry to prove Harnack inequality for classical solutions to the extension equation. This in turn implies Harnack inequality for solutions to the fractional Poisson problem. This work is joint with Pablo Raúl Stinga (Iowa State University).
Location: PMA 10.176

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