At the close of the 1980s, the independent contributions of Yann Brenier, Mike Cullen and
John Mather launched a revolution in the venerable field of optimal transport founded by G …

A PDE proof is provided for the sharp L^∞ estimates for the complex Monge-Ampère
equation that had required pluripotential theory before. The proof covers both cases of fixed …

By studying a negative gradient flow of certain Hessian functionals we establish the
existence of critical points of the functionals and consequently the existence of ground states …

Sharp L^∞ estimates are obtained for general classes of fully non-linear PDE's on non-
Kähler manifolds, complementing the theory developed earlier by the authors in joint work …

Pointwise gradient bounds via Riesz potentials, such as those available for the linear
Poisson equation, actually hold for general quasilinear degenerate equations of p …

The k-Hessian is the k-trace, or the kth elementary symmetric polynomial of eigenvalues of
the Hessian matrix. When k≥ 2, the k-Hessian equation is a fully nonlinear partial …

We derive a priori second-order estimates for solutions of a class of fully nonlinear elliptic
equations on Riemannian manifolds under structure conditions which are close to optimal …

In this paper, we establish weak continuity results for quasilinear elliptic and subelliptic
operators of divergence form, acting on corresponding classes of subharmonic functions …

Weak solutions to the complex Hessian equation Page 1 ANNA L E S D E L’INSTITU T FO
U RIER ANNALES DE L’INSTITUT FOURIER Zbigniew BLOCKI Weak solutions to the …

We prove some L∞ a priori estimates as well as existence and stability theorems for the
weak solutions of the complex Hessian equations in domains of ℂ n and on compact Kähler …