9 papers
Viscosity Solutions in Martinet Spaces
Thomas Bieske, Frederic Bowen
In this paper, we establish the properties of viscosity solutions in Martinet spaces, which lack both the algebraic group law of Carnot groups and the triangular vector fields of G…
Generalizations of the Drift Laplace Equation over the Quaternions in a Class of Grushin-Type Spaces
Thomas Bieske, Keller Blackwell
Beals, Gaveau, and Greiner in 1996 establish a formula for the fundamental solution to the Laplace equation with drift term in Grushin-type planes. The first author and Childers in…
Generalizations of the Drift Laplace Equation in the Heisenberg Group and a Class of Grushin-Type Spaces
Thomas Bieske, Keller Blackwell
We find fundamental solutions to p-Laplace equations with drift terms in the Heisenberg group and Grushin-type planes. These solutions are natural generalizations to the fundamenta…
Polarizing Anisotropic Heisenberg Groups
Thomas Bieske
We expand the class of polarizable Carnot groups by implementing a technique to polarize anisotropic Heisenberg groups.
The Fundamental Solution to the p-Laplacian in a class of Hörmander Vector Fields
Thomas Bieske, Robert D. Freeman
We find the fundamental solution to the p-Laplace equation in a class of Hörmander vector fields that generate neither a Carnot group nor a Grushin-type space. The singularity occu…
The -equation in Riemannian Vector Fields
Thomas Bieske
We employ Riemannian jets which are adapted to the Riemannian geometry to obtain the existence-uniqueness of viscosity solutions to the -Laplace equation in Riemannian v…
The -equation in Grushin-type Spaces
Thomas Bieske
We employ Grushin jets which are adapted to the geometry of Grushin-type spaces to obtain the existence-uniqueness of viscosity solutions to the -Laplace equation in Gru…
The Parabolic Infinite-Laplace Equation in Carnot groups
Thomas Bieske, Erin Martin
By employing a Carnot parabolic maximum principle, we show existence-uniqueness of viscosity solutions to a class of equations modeled on the parabolic infinite Laplace equation in…
Generalizations of a Laplacian-Type Equation in the Heisenberg Group and a Class of Grushin-Type Spaces
Thomas Bieske, Kristen Childers
Beals, Gaveau and Greiner (1996) find the fundamental solution to a 2-Laplace-type equation in a class of sub-Riemannian spaces. This solution is related to the well-known fundamen…