3 citations · 5 across the 7 of their papers we have counts for
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Infinity-harmonic functions in the plane: Regularity by injectivity
Karl K. Brustad
It has been a long standing conjecture that the -harmonic functions in the plane have a 1/3-Hölder continuous gradient. It \emph{is} known that solutions are and…
The Infinity-Potential in the Square
Karl K. Brustad
A representation formula for the solution of the -Laplace equation is constructed in a punctured square, the prescribed boundary values being on the sides and a…
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…