NOTES ON THE p-LAPLACE EQUATION (SECOND EDITION) Page 1 UNIVERSITY OF
JYVÄSKYLÄ DEPARTMENT OF MATHEMATICS AND STATISTICS REPORT 161 …

The most important partial differential equation of the second order is the celebrated Laplace
equation. This is the prototype for linear elliptic equations. It is less well known that it also …

The fundamental works of Doob, Hunt, Kakutani, Kolmogorov and many others have shown
the profound and powerful connection between the classical linear potential theory and the …

Given a weighted graph with N vertices, consider a real-valued regression problem in a
semi-supervised setting, where one observes n labeled vertices, and the task is to label the …

The purpose of this book is to give a quick and elementary, yet rigorous, presentation of the
rudiments of the so-called theory of Viscosity Solutions which applies to fully nonlinear 1st …

We study the consistency of Lipschitz learning on graphs in the limit of infinite unlabeled
data and finite labeled data. Previous work has conjectured that Lipschitz learning is well …

Calculus of Variations Page 1 Calc. Var. (2011) 42:289–299 DOI 10.1007/s00526-010-0388-1
Calculus of Variations Everywhere differentiability of infinity harmonic functions Lawrence C …

We study the PDE λ j (D 2 u)= 0, in Ω, with u= g, on∂ Ω. Here λ 1 (D 2 u)≤...≤ λ N (D 2 u)
are the ordered eigenvalues of the Hessian D 2 u. First, we show a geometric interpretation …

Lipschitz learning is a graph-based semisupervised learning method where one extends
labels from a labeled to an unlabeled data set by solving the infinity Laplace equation on a …

Extending the well-known connection between classical linear potential theory and
probability theory (through the interplay between harmonic functions and martingales) to the …