60 citations · 402 across the 74 of their papers we have counts for
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Smooth Solutions to a Class of Mixed Type Monge-Ampere Equations
Qing Han, Marcus Khuri
We prove the existence of C^{\infty} local solutions to a class of mixed type Monge-Ampere equations in the plane. More precisely, the equation changes type to finite order across…
Boundary Value Problems for Mixed Type Equations and Applications
Marcus A. Khuri
In this paper we outline a general method for finding well-posed boundary value problems for linear equations of mixed elliptic and hyperbolic type, which extends previous techniqu…
On the Local Isometric Embedding in R^3 of Surfaces with Gaussian Curvature of Mixed Sign
Qing Han, Marcus Khuri
We study the old problem of isometrically embedding a 2-dimensional Riemannian manifold into Euclidean 3-space. It is shown that if the Gaussian curvature vanishes to finite order…
The Local Isometric Embedding in R^3 of Two-Dimensional Riemannian Manifolds With Gaussian Curvature Changing Sign to Finite Order on a Curve
Marcus A. Khuri
We consider two natural problems arising in geometry which are equivalent to the local solvability of specific equations of Monge-Ampere type. These two problems are: the local iso…
Local Solvability of a Class of Degenerate Monge-Ampere Equations and Applications to Geometry
Marcus A. Khuri
We consider two natural problems arising in geometry which are equivalent to the local solvability of specific equations of Monge-Ampere type. These are: the problem of locally pre…
Counterexamples to the Local Solvability of Monge-Ampere Equations in the Plane
Marcus A. Khuri
In this paper, we present smooth examples of degenerate hyperbolic and mixed type Monge-Ampere equations in the plane, which do not admit a local C^3 solution.