Failure of Fatou type theorems for solutions to PDE of p-Laplace type in domains with flat boundaries

Abstract

Abstract Let denote Euclidean n space and given k a positive integer let be a k-dimensional plane with If we first study the Martin boundary problem for solutions to the p-Laplace equation (called p-harmonic functions) in relative to We then use the results from our study to extend the work of Wolff on the failure of Fatou type theorems for p-harmonic functions in to p-harmonic functions in when Finally, we discuss generalizations of our work to solutions of p-Laplace type PDE (called -harmonic functions).