講座編號：jz-yjsb-2021-y029
講座題目：Existence and qualitative analysis for nonlocal equations
主 講 人：楊敏波 教授 浙江師范大學(xué)
講座時(shí)間：2021年06月28日（星期一）上午10:00
講座地點(diǎn)：騰訊會(huì)議，會(huì)議ID：379 886 707
參加對象：數(shù)學(xué)與統(tǒng)計(jì)學(xué)院全體教師及研究生
主辦單位：數(shù)學(xué)與統(tǒng)計(jì)學(xué)院、研究生院
主講人簡介：
浙江師范大學(xué)教授，博士生導(dǎo)師，數(shù)學(xué)與計(jì)算機(jī)科學(xué)學(xué)院副院長，浙江省高校中青年學(xué)科帶頭人。主要從事非線性分析及其應(yīng)用領(lǐng)域的研究，主持或參與多項(xiàng)國家與省級科研項(xiàng)目，完成巴西國家科學(xué)技術(shù)發(fā)展委員會(huì)CNPq項(xiàng)目一項(xiàng)。在CVPDE、JDE、Com. Anal. Geometry、Nonlinearity、 DCDS-A 等雜志發(fā)表論文六十余篇。
主講內(nèi)容：
The aim of this talk is to introduce some classification results of the solutions for the critical nonlocal equations due to the weighted Hardy-Littlewood-Sobolev inequality and Sobolev imbedding. We prove the existence of positive ground state solutions for the subcritical case by using Schwarz symmetrization and the critical case by a nonlocal version of concentration-compactness principle. We also establish the regularity of positive solutions for these two equations. Finally, we prove the symmetry of positive solutions by the moving plane method in integral forms.