报告题目1: Boundary Calderon-Zygmund estimates and Whitney decomposition
报告人:李雪梅 博士(西安交通大学)
报告时间:2023年9月18日9:30—10:30
报告地点:线上报告(腾讯会议:560-773-589)
主办单位:永利澳门网站平台
报告摘要: In this talk, we will establish boundary Calderon-Zygmund estimates for elliptic and parabolic equations on $C^{1,\alpha}$ domains. Instead of straightening the boundary, we derive boundary $W^{2,p}$ estimates from the interior $W^{2,p}$ estimates and the boundary $C^{1,\alpha}$ estimates by Whitney decomposition.
报告题目2: Regularity for degenerate fully nonlinear elliptic equations
报告人:李雪梅 博士(西安交通大学)
报告时间:2023年9月18日10:30-11:30
报告地点:线上报告(腾讯会议:560-773-589)
主办单位:永利澳门网站平台
报告摘要: In this talk, we will investigate $C^{1,\alpha}$ and $W^{2,\delta}$ regularity for degenerate fully nonlinear elliptic equations in form $|Du|^\gamma F(D^2 u)=f$, where $\gamma>0$. Boundary ${{C}^{1,\alpha}}$ estimates on ${{C}^{1,\alpha}}$ domains are obtained by compactness and perturbation technique. In addition, we construct counterexamples to show that $W^{2,\delta}$ regularity doesn't hold for any $\delta>0$.
报告题目3: Regularity for singular fully nonlinear elliptic equations
报告人:李雪梅 博士(西安交通大学)
报告时间:2023年9月18日14:30-15:30
报告地点:线上报告(腾讯会议:560-773-589)
主办单位:永利澳门网站平台
报告摘要: In this talk, we will investigate $C^{1,\alpha}$ and $W^{2,\delta}$ regularity for singular fully nonlinear elliptic equations in form $|Du|^\gamma F(D^2 u)=f$, where $\gamma<0$. Boundary ${{C}^{1,\alpha}}$ estimates on ${{C}^{1,\alpha}}$ domains are obtained by compactness and perturbation technique. In addition, we obtain boundary $W^{2,\delta}$ regularity on ${{C}^{1,\alpha}}$ domains.
报告题目4: Asymptotic behavior of solutions of Monge-Ampere equations
报告人:李雪梅 博士(西安交通大学)
报告时间:2023年9月18日15:30-16:30
报告地点:线上报告(腾讯会议:560-773-589)
主办单位:永利澳门网站平台
报告摘要: In this talk, we will investigate the asymptotic behavior at infinity of convex viscosity solutions of Monge-Ampere equations in half spaces. The quadratic growth condition and Pogorelov estimates are utilized.
报告人简介:李雪梅,西安交通大学博士。从事偏微分方程正则性理论方面的研究,目前在Mathematische Annalen, Journal of Functional Analysis, Comptes Rendus. Mathématique发表三篇SCI论文.