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.

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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