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The dirichlet problem for nonlinear second‐order elliptic equations I. Monge‐ampégre equation

https://doi.org/10.1002/cpa.3160370306
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What this work says

Outgoing claims: the papers this work cites, builds on, or argues with.

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Estimates near the boundary for solutions of elliptic partial differential equations satisfying general boundary conditions. I
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On the regularity of the solution of the n ‐dimensional Minkowski problem
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On the regularity of the monge‐ampère equation det (∂ 2 u/∂x i ∂x j ) = f(x, u)
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Classical solutions of fully nonlinear, convex, second‐order elliptic equations
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A symmetry problem in potential theory
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Symmetry and related properties via the maximum principle
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Équations du type de Monge—Ampère sur les variétés Riemanniennes compactes, II
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Équations de Monge—Ampère réelles
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BOUNDEDLY NONHOMOGENEOUS ELLIPTIC AND PARABOLIC EQUATIONS
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BOUNDEDLY NONHOMOGENEOUS ELLIPTIC AND PARABOLIC EQUATIONS IN A DOMAIN
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ON DEGENERATE NONLINEAR ELLIPTIC EQUATIONS
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Fully Nonlinear, Uniformly Elliptic Equations Under Natural Structure Conditions
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Improper affine hyperspheres of convex type and a generalization of a theorem by K. Jörgens.

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Incoming claims: where this work appears in other papers’ reference lists and arguments.

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Remarks on a planar conformal curvature problem
inferred← citeshttps://doi.org/10.1007/s00605-025-02131-9openalex-snapshot
On the general Orlicz-logarithmic Minkowski problems in the plane
inferred← citeshttps://doi.org/10.1007/s10114-008-6010-1openalex-snapshot
Spacelike hypersurfaces of prescribed Gauss-Kronecker curvature in exterior domains
inferred← citeshttps://doi.org/10.1007/s10114-009-7063-5openalex-snapshot
The affine complete hypersurfaces of constant Gauss-Kronecker curvature
inferred← citeshttps://doi.org/10.1007/s10114-019-7524-4openalex-snapshot
Boundary Behavior of Large Solutions to the Monge-Ampère Equation in a Borderline Case
inferred← citeshttps://doi.org/10.1007/s10114-021-0340-7openalex-snapshot
The Neumann Problem for Parabolic Hessian Quotient Equations
inferred← citeshttps://doi.org/10.1007/s10231-008-0083-4openalex-snapshot
Stability of radial symmetry for a Monge-Ampère overdetermined problem
inferred← citeshttps://doi.org/10.1007/s10231-012-0295-5openalex-snapshot
Stability of isoperimetric type inequalities for some Monge–Ampère functionals
inferred← citeshttps://doi.org/10.1007/s10231-020-01027-9openalex-snapshot
Maximum principles and the method of moving planes for the uniformly elliptic nonlocal Bellman operator and applications
inferred← citeshttps://doi.org/10.1007/s10240-008-0013-4openalex-snapshot
Geometry of Kähler metrics and foliations by holomorphic discs
inferred← citeshttps://doi.org/10.1007/s10255-017-0683-0openalex-snapshot
Asymptotic behaviour of hessian equation with boundary blow up
inferred← citeshttps://doi.org/10.1007/s10255-022-1024-5openalex-snapshot
A Class of Singular Coupled Systems of Superlinear Monge-Ampère Equations
inferred← citeshttps://doi.org/10.1007/s10455-023-09933-wopenalex-snapshot
Boundary properties for a Monge-Ampère equation of prescribed affine Gauss curvature
inferred← citeshttps://doi.org/10.1007/s10473-022-0518-9openalex-snapshot
A Subsolution Theorem for the Monge-Ampère Equation over an Almost Hermitian Manifold
inferred← citeshttps://doi.org/10.1007/s10473-024-0520-5openalex-snapshot
A singular Dirichlet problem for the Monge-Ampère type equation
inferred← citeshttps://doi.org/10.1007/s10711-010-9567-7openalex-snapshot
Moduli of flat conformal structures of hyperbolic type
inferred← citeshttps://doi.org/10.1007/s10711-012-9779-0openalex-snapshot
Curvature flow of complete hypersurfaces in hyperbolic space
inferred← citeshttps://doi.org/10.1007/s10711-013-9921-7openalex-snapshot
Compactness for immersions of prescribed Gaussian curvature II: geometric aspects
inferred← citeshttps://doi.org/10.1007/s10915-008-9221-9openalex-snapshot
Vanishing Moment Method and Moment Solutions for Fully Nonlinear Second Order Partial Differential Equations
inferred← citeshttps://doi.org/10.1007/s10915-012-9617-4openalex-snapshot
Quadratic Finite Element Approximations of the Monge-Ampère Equation
inferred← citeshttps://doi.org/10.1007/s10915-016-0220-yopenalex-snapshot
On Standard Finite Difference Discretizations of the Elliptic Monge–Ampère Equation
inferred← citeshttps://doi.org/10.1007/s10915-018-0698-6openalex-snapshot
A Least-Squares/Relaxation Method for the Numerical Solution of the Three-Dimensional Elliptic Monge–Ampère Equation
inferred← citeshttps://doi.org/10.1007/s10915-023-02183-9openalex-snapshot
Trivariate Spline Collocation Methods for Numerical Solution to 3D Monge-Ampère Equation
inferred← citeshttps://doi.org/10.1007/s10915-026-03252-5openalex-snapshot
Error Analysis of Legendre Spectral Methods for the Monge-Ampère Equation on Convex Quadrilaterals and Hexahedra
inferred← citeshttps://doi.org/10.1007/s10958-011-0577-2openalex-snapshot
On the classical solvability of the Dirichlet problem for nondegenerate m-Hessian equations
inferred← citeshttps://doi.org/10.1007/s10958-014-2016-7openalex-snapshot
From Gårding’s Cones to p-Convex Hypersurfaces
inferred← citeshttps://doi.org/10.1007/s11118-005-0915-4openalex-snapshot
Regularity of Degenerate Monge–Ampère and Prescribed Gaussian Curvature Equations in Two Dimensions
inferred← citeshttps://doi.org/10.1007/s11118-022-10009-wopenalex-snapshot
Uniform Estimates for Concave Homogeneous Complex Degenerate Elliptic Equations Comparable to the Monge-Ampère Equation
inferred← citeshttps://doi.org/10.1007/s11401-016-0973-5openalex-snapshot
An initial-boundary value problem for parabolic Monge-Ampère equation in mathematical finance
inferred← citeshttps://doi.org/10.1007/s11401-020-0220-yopenalex-snapshot
A Unified Boundary Behavior of Large Solutions to Hessian Equations
inferred← citeshttps://doi.org/10.1007/s11401-025-0045-9openalex-snapshot
Boundary Behavior of Large Solutions for Equations of Monge-Ampère Type
inferred← citeshttps://doi.org/10.1007/s11425-019-1691-1openalex-snapshot
Global regularity for a class of Monge-Ampère type equations
inferred← citeshttps://doi.org/10.1007/s11425-023-2275-1openalex-snapshot
A class of Hessian quotient equations in warped product manifolds
inferred← citeshttps://doi.org/10.1007/s11425-024-2424-yopenalex-snapshot
On local solubility of Bao-Ratiu equations on surfaces related to the geometry of the diffeomorphism group
inferred← citeshttps://doi.org/10.1007/s11464-011-0109-xopenalex-snapshot
On uniqueness and existence of viscosity solutions to Hessian equations in exterior domains
inferred← citeshttps://doi.org/10.1007/s11464-013-0340-8openalex-snapshot
Existence of viscosity solutions for Hessian equations in exterior domains
inferred← citeshttps://doi.org/10.1007/s11464-020-0045-8openalex-snapshot
The Optimal Global Estimates and Boundary Behavior for Large Solutions to the k-Hessian Equation
inferred← citeshttps://doi.org/10.1007/s11512-006-0029-2openalex-snapshot
On the behavior of strictly plurisubharmonic functions near real hypersurfaces
inferred← citeshttps://doi.org/10.1007/s11587-009-0058-9openalex-snapshot
Isoperimetric estimates for eigenfunctions of Hessian operators
inferred← citeshttps://doi.org/10.1007/s11784-009-0107-8openalex-snapshot
Some remarks on singular solutions of nonlinear elliptic equations. I
inferred← citeshttps://doi.org/10.1007/s11784-013-0151-2openalex-snapshot
On some properties of the positive m-Hessian operators in C 2(Ω)
inferred← citeshttps://doi.org/10.1007/s11784-015-0217-4openalex-snapshot
On algebraic and geometric conditions in the theory of Hessian equations
inferred← citeshttps://doi.org/10.1007/s11784-021-00922-9openalex-snapshot
Boundary blow-up solutions to the k-Hessian equation with the logarithmic nonlinearity and singular weights
inferred← citeshttps://doi.org/10.1007/s11856-016-1329-2openalex-snapshot
Dirichlet problem of quaternionic Monge–Ampère equations
inferred← citeshttps://doi.org/10.1007/s12220-009-9086-7openalex-snapshot
Hypersurfaces of Constant Curvature in Hyperbolic Space I
inferred← citeshttps://doi.org/10.1007/s12220-012-9300-xopenalex-snapshot
Curvature Flow of Complete Convex Hypersurfaces in Hyperbolic Space
inferred← citeshttps://doi.org/10.1007/s12220-012-9332-2openalex-snapshot
Lipschitz Continuous Viscosity Solutions for a Class of Fully Nonlinear Equations on Lie Groups
inferred← citeshttps://doi.org/10.1007/s12220-015-9606-6openalex-snapshot
Starshaped Locally Convex Hypersurfaces with Prescribed Curvature and Boundary
inferred← citeshttps://doi.org/10.1007/s12220-016-9739-2openalex-snapshot
Global $$W^{1,p}$$ estimates for solutions to the linearized Monge–Ampère equations
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