TY - JOUR
T1 - A Dirichlet's principle for the k-Hessian
AU - Case, Jeffrey S.
AU - Wang, Yi
PY - 2018/12/1
Y1 - 2018/12/1
N2 - The k-Hessian operator σk is the k-th elementary symmetric function of the eigenvalues of the Hessian. It is known that the k-Hessian equation σk(D2u)=f with Dirichlet boundary condition u=0 is variational; indeed, this problem can be studied by means of the k-Hessian energy −∫uσk(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.
AB - The k-Hessian operator σk is the k-th elementary symmetric function of the eigenvalues of the Hessian. It is known that the k-Hessian equation σk(D2u)=f with Dirichlet boundary condition u=0 is variational; indeed, this problem can be studied by means of the k-Hessian energy −∫uσk(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.
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U2 - 10.1016/j.jfa.2018.08.024
DO - 10.1016/j.jfa.2018.08.024
M3 - Article
AN - SCOPUS:85053164621
VL - 275
SP - 2895
EP - 2916
JO - Journal of Functional Analysis
JF - Journal of Functional Analysis
SN - 0022-1236
IS - 11
ER -