Soufian Abja

activity

20172021

collaborators

4 papers

math.AP2021

Local regularity for concave homogeneous complex degenerate elliptic equations comparable to the Monge-Ampère equation

Soufian Abja, Guillaume Olive

In this paper, we establish a local regularity result for $W_{loc}^{2, p}$ solutions to complex degenerate nonlinear elliptic equations $F (D_{C}^{2} u) = f$ when they…

math.AP2020

Uniform estimates for concave homogeneous complex degenerate elliptic equations comparable to the Monge-Ampère equation

Soufian Abja, Sławomir Dinew, Guillaume Olive

We prove sharp uniform estimates for strong supersolutions of a large class of fully nonlinear degenerate elliptic complex equations. Our findings rely on ideas of Kuo and Trudinge…

math.CV2019

Regularity of geodesics in the spaces of convex and plurisubharmonic functions

Soufian Abja, Slawomir Dinew

In this note we investigate the regularity of geodesics in the space of convex and plurisubharmonic functions. In the real setting we prove (optimal) local C^{1,1} regularity. We c…

math.CV2017

Geometry and Topology of the space of plurisubharmonic functions

Soufian Abja

Let $Ω$ be a strongly pseudoconvex domain. We introduce the Mabuchi space of strongly plurisubharmonic functions in $Ω$ . We study metric properties of this space using Mabuchi geod…