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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 Note On Determining Projections for Non-Homogeneous Incompressible Fluids
Benjamin Faktor, Michael Holst
In this note, we consider a viscous incompressible fluid in a finite domain in both two and three dimensions, and examine the question of determining degrees of freedom (projection…
Some Remarks on the Space of Locally Sobolev-Slobodeckij Functions
A. Behzadan, M. Holst
The study of certain differential operators between Sobolev spaces of sections of vector bundles on compact manifolds equipped with rough metric is closely related to the study of…
Generalized Solutions to Semilinear Elliptic PDE with Applications to the Lichnerowicz Equation
Michael Holst, Caleb Meier
In this article we investigate the existence of a solution to a semilinear, elliptic, partial differential equation with distributional coefficients and data. The problem we consid…
A Nonlinear Elasticity Model of Macromolecular Conformational Change Induced by Electrostatic Forces
Yongcheng Zhou, Michael Holst, James Andrew McCammon
In this paper we propose a nonlinear elasticity model of macromolecular conformational change (deformation) induced by electrostatic forces generated by an implicit solvation model…
Determining Projections and Functionals for Weak Solutions of the Navier-Stokes Equations
Michael Holst, Edriss Titi
In this paper we prove that an operator which projects weak solutions of the two- or three-dimensional Navier-Stokes equations onto a finite-dimensional space is determining if it…