Tuesday, November 3, 2009
10:30 AM in REC 307
Panki Kim
Department of Mathematical Sciences, Seoul National University (Korea) Visiting the Department of Mathematics, University of Illinois at Urbana-Champaign

The boundary Harnack principle of the independent sum of a Brownian motion and a symmetric stable process

Abstract

In this talk, we consider the family of pseudo differential operators {Δ + b Δα/2; b∈ [0, 1]}$ that evolves continuously from Δ to Δ+ Δα2. We establish a uniform boundary Harnack principle with explicit boundary decay rate for nonnegative functions which are harmonic with respect to Δ +b = Δα/2 (or equivalently, the sum of a Brownian motion and an independent symmetric α-stable process with constant multiple b1/α) in C1, 1 open sets.

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