Title: Partial Differential Equations and Applied Mathematics Seminar (2016.12.9)

Author: CMAC

Date: 2016-12-06 (14:13)

Date/Time: Dec., 9th, Fri., 4:00 ~ 5:00 PM

Location: Science Building #225 Yonsei University

Speaker: 김유찬 박사

Affiliation: NIMS

Title: Potential type estimates for nonlinear elliptic equations

Abstract:

We consider nonlinear elliptic equations $div a(Du,u,x)=\mu$ in $\Omega$ in a general setting that the nonlinearity depends on the possibly unbounded solution itself. We obtain an optimal point-wise estimate for the gradient in terms of a certain Riesz potential, $|Du(0)|\leq c\int_{Q_{r}}|Du|dx+c\int_{0}^{r}\frac{|\mu|(Q_{\rho})}{\rho^{n-1}}\frac{d\rho}{\rho}$