# A fully nonlinear Sobolev trace inequality

@article{Case2016AFN, title={A fully nonlinear Sobolev trace inequality}, author={Jeffrey S. Case and Yi Wang}, journal={arXiv: Analysis of PDEs}, year={2016} }

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 $\sigma_k(D^2u)=f$ with Dirichlet boundary condition $u=0$ is variational; indeed, this problem can be studied by means of the $k$-Hessian energy $-\int u\sigma_k(D^2u)$. 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… Expand

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