Article ID | Journal | Published Year | Pages | File Type |
---|---|---|---|---|
11012924 | Journal of Functional Analysis | 2018 | 22 Pages |
Abstract
The k-Hessian operator Ïk is the k-th elementary symmetric function of the eigenvalues of the Hessian. It is known that the k-Hessian equation Ïk(D2u)=f with Dirichlet boundary condition u=0 is variational; indeed, this problem can be studied by means of the k-Hessian energy ââ«uÏk(D2u). 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 establish a Dirichlet's principle for k-admissible functions with prescribed Dirichlet boundary data.
Related Topics
Physical Sciences and Engineering
Mathematics
Algebra and Number Theory
Authors
Jeffrey S. Case, Yi Wang,