题目: A fully nonlinear Sobolev trace inequality

报告人：WANG Yi（Johns Hopkins University）

时间: July 4th, 4:00-5:00

地点: 管研楼1518

摘要: The $k$-Hessian operator $/sigma_k$ is the $k$-th elementary symmetric function of the eigenvalues of the Hessian. It is known that the $k$-Hessian equation $/sigma_k(D^2 u)=f$ with Dirichlet boundary condition $u=0$ is variational; indeed, this problem can be studied by means of the $k$-Hessian energy $/int -u /sigma_k(D^2 u)$. We construct a natural boundary functional which, when added to the $k$-Hessian energy, yields as its critical points solutions of $k$-Hessian equations with general non-vanishing boundary data. As a consequence, we prove a sharp Sobolev trace inequality for $k$-admissible functions $u$ which estimates the $k$-Hessian energy in terms of the boundary values of $u$. This is joint work with Jeffrey Case.

欢迎广大师生参加！