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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 |
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Vol. 12 (2019), No. 2, 505–535
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DOI: 10.2140/apde.2019.12.505
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Abstract |
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A viscosity approach is introduced for the Dirichlet problem associated to complex Hessian-type equations on domains in . 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. |
Keywords
nonlinear elliptic PDEs, viscosity solutions,
pluripotential theory
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Mathematical Subject Classification 2010
Primary: 35J70
Secondary: 32U15
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Milestones
Received: 13 January 2018
Accepted: 30 May 2018
Published: 14 August 2018
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Authors |
| Sławomir Dinew | |
| Institute of Mathematics Jagiellonian University Kraków Poland |
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| Hoang-Son Do | |
| Institute of Mathematics Vietnam Academy of Science and Technology Hanoi Vietnam |
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| Tat Dat Tô | |
| Institut Mathématiques de
Toulouse Université Paul Sabatier Toulouse France |
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