Vol. 12, No. 2, 2019

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A viscosity approach to the Dirichlet problem for degenerate complex Hessian-type equations

Sławomir Dinew, Hoang-Son Do and Tat Dat Tô

Vol. 12 (2019), No. 2, 505–535
DOI: 10.2140/apde.2019.12.505

A viscosity approach is introduced for the Dirichlet problem associated to complex Hessian-type equations on domains in n . The arguments are modeled on the theory of viscosity solutions for real Hessian-type equations developed by Trudinger (1990). As a consequence we solve the Dirichlet problem for the Hessian quotient and special Lagrangian equations. We also establish basic regularity results for the solutions.

nonlinear elliptic PDEs, viscosity solutions, pluripotential theory
Mathematical Subject Classification 2010
Primary: 35J70
Secondary: 32U15
Received: 13 January 2018
Accepted: 30 May 2018
Published: 14 August 2018
Sławomir Dinew
Institute of Mathematics
Jagiellonian University
Hoang-Son Do
Institute of Mathematics
Vietnam Academy of Science and Technology
Tat Dat Tô
Institut Mathématiques de Toulouse
Université Paul Sabatier