Level set methods are a popular and powerful class of numerical algorithms for dynamic
implicit surfaces and solution of Hamilton-Jacobi PDEs. While the advanced level set …

Convergent numerical schemes for degenerate elliptic partial differential equations are
constructed and implemented. Simple conditions are identified which ensure that nonlinear …

The elliptic Monge–Ampère equation is a fully nonlinear partial differential equation that
originated in geometric surface theory and has been applied in dynamic meteorology …

Certain fully nonlinear elliptic Partial Differential Equations can be written as functions of the
eigenvalues of the Hessian. These include: the Monge-Ampere equation, Pucci's Maximal …

In the continuum, close connections exist between mean curvature flow, the Allen-Cahn
(AC) partial differential equation, and the Merriman-Bence-Osher (MBO) threshold dynamics …

The theory of viscosity solutions has been effective for representing and approximating weak
solutions to fully nonlinear partial differential equations such as the elliptic Monge--Ampère …

We show that a broad class of fully nonlinear, second‐order parabolic or elliptic PDEs can
be realized as the Hamilton‐Jacobi‐Bellman equations of deterministic two‐person games …

We build convergent discretizations and semi-implicit solvers for the Infinity Laplacian and
the game theoretical p-Laplacian. The discretizations simplify and generalize earlier ones …

In this article, we study the well-posedness (uniqueness and existence of solutions) of
nonlinear elliptic Partial Differential Equations (PDEs) on a finite graph. These results are …

We review level set methods and the related techniques that are common in many PDE-
based image models. Many of these techniques involve minimizing the total variation of the …