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：威廉希尔中文网站

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：威廉希尔中文网站

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：威廉希尔中文网站

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：威廉希尔中文网站

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.