3 citations · 5 across the 6 of their papers we have counts for
7 papers
Sobolev gradients of viscosity supersolutions
Karl K. Brustad
We investigate which elliptic PDEs that have the property that every viscosity supersolution is , . The asymptotic cone of the operator's…
The one-dimensional nonlocal Dominative -Laplace equation
Karl K. Brustad
The explicit solution to the Dirichlet problem for a class of mean value equations on the real line is derived. It shed some light on the behavior of solutions to general nonlocal…
Segre's Theorem. An analytic proof of a result in differential geometry
Karl K. Brustad
We present an analytic approach on how to solve the problem , , in connected domains .
Total derivatives of eigenvalues and eigenprojections of symmetric matrices
Karl K. Brustad
Conditions for existence and formulas for the first- and second order total derivatives of the eigenvalues, and the first order total derivatives of the eigenprojections of smooth…
A discrete stochastic interpretation of the Dominative -Laplacian
Karl K. Brustad, Peter Lindqvist, Juan J. Manfredi
The Dominative -Laplacian is the operator defined for as follows: \begin{equation}\label{dominativep} \mathcal{L}_{p}u(x)=\frac{1}{p}\left(λ_{1}+\ldots+λ_{N-1}…
Sublinear Elliptic Operators
Karl K. Brustad
We investigate second order elliptic equations \[F(\mathcal{H}u) = 0\] where the function on the space of symmetric matrices is assumed to b…