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Joint Princeton-Rutgers Seminar on Geometric PDE's

A fully nonlinear Sobolev trace inequality

Location:  Princeton - Fine Hall 224
Date & time: Friday, 21 October 2016 at 3:30PM -

Yi Wang, Johns Hopkins University

"A fully nonlinear Sobolev trace inequality"

Time: 3:30 PM

Location: Princeton - Fine Hall 224

Abstract: 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.

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