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 …

In this paper we present the basic theory of the Monge-Ampere equation together with a
selection of geometric applications, mainly to affine geometry. First we introduce the Monge …

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 …

In our previous paper on this topic, we introduced the notion of k-Hessian measure
associated with a continuous k-convex function in a domain Ω in Euclidean n-space, k= 1 …

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 Liouville-Bratu-Gelfand Problem for Radial Operators Page 1 Journal of Differential
Equations 184, 283–298 (2002) doi:10.1006/jdeq.2001.4151 The Liouville^Bratu^Gelfand …

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 …

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

In this paper, we establish the results of nonexistence and existence of blow-up radial
solutions for a k-Hessian equation with a nonlinear operator. Under some suitable growth …

The existence problem is solved, and global pointwise estimates of solutions are obtained
for quasilinear and Hessian equations of Lane-Emden type, including the following two …