6 papers
Nonuniqueness of solutions to the Lagrangian mean curvature equation
Arunima Bhattacharya, W. Jacob Ogden
We resolve a question posed by Harvey and Lawson concerning the uniqueness of continuous viscosity solutions to the Dirichlet problem for the Lagrangian mean curvature equation on…
Optimal Regularity for Hölder continuous Hamiltonian Stationary Lagrangian graphs
Arunima Bhattacharya, W. Jacob Ogden
In this paper, we establish optimal regularity for Hölder continuous Hamiltonian stationary Lagrangian graphs in . We prove that such a graph is smooth whenever its H…
Grim Raindrop: A Translating Solution to Curve Diffusion Flow
W. Jacob Ogden, Micah Warren
We show the existence of a properly immersed translating solution to curve diffusion flow in the plane. Curve diffusion flow is a higher order version of curve shortening flow, nam…
Remarks on the Complex Euler Equations
Dallas Albritton, W. Jacob Ogden
We consider a complexification of the Euler equations introduced by Šverák which conserves energy. We prove that these complex Euler equations are nonlinearly ill-posed below analy…
Sobolev and Schatten Estimates for the Complex Green Operator on Spheres
Elena Kim, W. Jacob Ogden, Tommie Reerink +1
The complex Green operator on CR manifolds is the inverse of the Kohn-Laplacian on the orthogonal complement of its kernel. In this note, we prove Schatte…
Polynomials on the Sierpinski Gasket with Respect to Different Laplacians which are Symmetric and Self-Similar
Christian Loring, W. Jacob Ogden, Ely Sandine +1
We study the analogue of polynomials (solutions to for some ) on the Sierpinski gasket () with respect to a family of symmetric, self-similar Laplacians const…