Concavity of the Lagrangian phase operator and applications

DOI10.1007/s00526-017-1191-zzbMath1378.35116arXiv1607.07194OpenAlexW2962874192MaRDI QIDQ2406051

Sebastien Picard, Xuan Wu, Tristan C. Collins

Publication date: 26 September 2017

Published in: Calculus of Variations and Partial Differential Equations (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1607.07194

zbMATH Keywords

Dirichlet problemLagrangian phase operator

Mathematics Subject Classification ID

Nonlinear elliptic equations (35J60) Lagrangian submanifolds; Maslov index (53D12) Other partial differential equations of complex analysis in several variables (32W50)

Related Items (18)

A viscosity approach to the Dirichlet problem for degenerate complex Hessian-type equations ⋮ The deformed Hermitian Yang-Mills equation on three-folds ⋮ On the Dirichlet problem for Lagrangian phase equation with critical and supercritical phase ⋮ The Cauchy-Dirichlet problem for parabolic deformed Hermitian-Yang-Mills equation ⋮ Fully nonlinear elliptic equations with gradient terms on compact almost Hermitian manifolds ⋮ Existence of entire solutions to the Lagrangian mean curvature equations in supercritical phase ⋮ High-order estimates for fully nonlinear equations under weak concavity assumptions ⋮ On the regularity of Hamiltonian stationary Lagrangian submanifolds ⋮ The inhomogeneous Dirichlet problem for natural operators on manifolds ⋮ Pseudoconvexity for the special Lagrangian potential equation ⋮ Tan-concavity property for Lagrangian phase operators and applications to the tangent Lagrangian phase flow ⋮ Unnamed Item ⋮ The Neumann problem of special Lagrangian equations with supercritical phase ⋮ Moment maps, nonlinear PDE and stability in mirror symmetry. I: Geodesics ⋮ Interior Schauder estimates for the fourth order Hamiltonian stationary equation in two dimensions ⋮ The Neumann problem for complex special Lagrangian equations with critical phase ⋮ The Neumann problem for special Lagrangian equations with critical phase ⋮ Gradient Bounds for Almost Complex Special Lagrangian Equation with Supercritical Phase

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