報(bào) 告 人：陳振慶 教授

報(bào)告題目：Boundary Harnack principle for diffusion processes with jumps

報(bào)告時(shí)間：2024年11月20日（星期三）下午3：30

報(bào)告地點(diǎn)：靜遠(yuǎn)樓1506學(xué)術(shù)報(bào)告廳

主辦單位：數(shù)學(xué)研究院、數(shù)學(xué)與統(tǒng)計(jì)學(xué)院、科學(xué)技術(shù)研究院

報(bào)告人簡(jiǎn)介：

       陳振慶，美國(guó)華盛頓大學(xué)（西雅圖）數(shù)學(xué)系教授，分別于2007年和2014年當(dāng)選為美國(guó)數(shù)理統(tǒng)計(jì)學(xué)會(huì)士(Fellow)和美國(guó)數(shù)學(xué)學(xué)會(huì)會(huì)士(Fellow)。陳振慶教授主要從事概率論及隨機(jī)過(guò)程的研究，主要的研究方向包括概率論以及隨機(jī)分析，馬爾可夫過(guò)程以及狄氏空間理論，隨機(jī)微分方程，擴(kuò)散過(guò)程，穩(wěn)定過(guò)程以及偏微分方程中的概率方法等。發(fā)表學(xué)術(shù)論文200余篇，學(xué)術(shù)專(zhuān)著兩部，國(guó)際期刊Potential Analysis的主編，2019年獲伊藤獎(jiǎng) (Ito Prize)。

報(bào)告摘要：

       The classical boundary Harnack principle asserts that two positive harmonic functions that vanish on a portion of the boundary of a smooth domain decay at the same rate. It is well known that scale invariant boundary Harnack inequality holds for Laplacian \Delta on uniform domains and holds for fractional Laplacians \Delta^s on any open sets. It has been an open problem whether the scale-invariant boundary Harnack inequality holds on bounded Lipschitz domains for Levy processes with Gaussian components such as the independent sum of a Brownian motion and an isotropic stable process (which corresponds to \Delta + \Delta^s).   

       In this talk, I will present a necessary and sufficient condition for the scale-invariant boundary Harnack inequality to hold for a class of diffusion processes with jumps on metric measure spaces. This result will then be applied to give a sufficient geometric condition for the scale-invariant boundary Harnack inequality to hold for subordinate Brownian motions having Gaussian components on bounded Lipschitz domains in Euclidean spaces. This condition is almost optimal and a counterexample will be given showing that the scale-invariant BHP may fail on some bounded Lipschitz domains with large Lipschitz constants. Based on joint work with Jieming Wang.