63 citations · 179 across the 14 of their papers we have counts for
14 papers
Optimal Control in Hilbert Complex Spaces with Finite Element Exterior Calculus
Farid Bozorgnia, Michael Holst, Anshu Kumar +3
We develop a framework for PDE-constrained optimal control on Hilbert complexes and its structure-preserving discretization by finite element exterior calculus (FEEC), with emphasi…
Regularity of solutions of the Navier-Stokes-αβ equations with wall-eddy boundary conditions
Nella Rotundo, Gantumur Tsogtgerel
We establish global well-posedness and regularity for the Navier-Stokes-αβ system endowed with the wall-eddy boundary conditions proposed by Fried and Gurtin (2008). These conditio…
A Scaling Approach to Elliptic Theory for Geometrically-Natural Differential Operators with Sobolev-Type Coefficients
Michael Holst, David Maxwell, Gantumur Tsogtgerel
We develop local elliptic regularity for operators having coefficients in a range of Sobolev-type function spaces (Bessel potential, Sobolev-Slobodeckij, Triebel-Lizorkin, Besov) w…
A prescribed scalar and boundary mean curvature problem and the Yamabe classification on asymptotically Euclidean manifolds with inner boundary
Vladmir Sicca, Gantumur Tsogtgerel
We consider the problem of finding a metric in a given conformal class with prescribed non-positive scalar curvature and non-positive boundary mean curvature on an asymptotically E…
On uniqueness of weak solutions to the second boundary value problem for generated prescribed Jacobian equations
Gerard Awanou, Gantumur Tsogtgerel
We prove that two Aleksandrov solutions of a generated prescribed Jacobian equation have the same gradients at points where they are both differentiable. For the optimal transporta…
A prescribed scalar and boundary mean curvature problem on compact manifolds with boundary
Vladmir Sicca, Gantumur Tsogtgerel
We consider the problem of finding a metric in a given conformal class with prescribed nonpositive scalar curvature and nonpositive boundary mean curvature on a compact manifold wi…
Convergence of Discrete Exterior Calculus Approximations for Poisson Problems
Erick Schulz, Gantumur Tsogtgerel
Discrete exterior calculus (DEC) is a framework for constructing discrete versions of exterior differential calculus objects, and is widely used in computer graphics, computational…
Axisymmetric critical points of a nonlocal isoperimetric problem on the two-sphere
Rustum Choksi, Ihsan Topaloglu, Gantumur Tsogtgerel
On the two dimensional sphere, we consider axisymmetric critical points of an isoperimetric problem perturbed by a long-range interaction term. When the parameter controlling the n…
Non-CMC Solutions of the Einstein Constraint Equations on Compact Manifolds with Apparent Horizon Boundaries
M. Holst, C. Meier, G. Tsogtgerel
In this article we continue our effort to do a systematic development of the solution theory for conformal formulations of the Einstein constraint equations on compact manifolds wi…
The Lichnerowicz equation on compact manifolds with boundary
Michael Holst, Gantumur Tsogtgerel
In this article we initiate a systematic study of the well-posedness theory of the Einstein constraint equations on compact manifolds with boundary. This is an important problem in…
On the consistency of the combinatorial codifferential
Douglas N. Arnold, Richard S. Falk, Johnny Guzmán +1
In 1976, Dodziuk and Patodi employed Whitney forms to define a combinatorial codifferential operator on cochains, and they raised the question whether it is consistent in the sense…
Local Convergence of Adaptive Methods for Nonlinear Partial Differential Equations
Michael Holst, Gantumur Tsogtgerel, Yunrong Zhu
In this article we develop convergence theory for a general class of adaptive approximation algorithms for abstract nonlinear operator equations on Banach spaces, and use the theor…
Far-from-constant mean curvature solutions of Einstein's constraint equations with positive Yamabe metrics
M. Holst, G. Nagy, G. Tsogtgerel
In this article we develop some new existence results for the Einstein constraint equations using the Lichnerowicz-York conformal rescaling method. The mean extrinsic curvature is…
Rough solutions of the Einstein constraints on closed manifolds without near-CMC conditions
Michael Holst, Gabriel Nagy, Gantumur Tsogtgerel
We consider the conformal decomposition of Einstein's constraint equations introduced by Lichnerowicz and York, on a closed manifold. We establish existence of non-CMC weak solutio…