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

Akman, Murat and Lewis, John and Vogel, Andrew (2022) Failure of Fatou type theorems for solutions to PDE of p-Laplace type in domains with flat boundaries. Working Paper. Communications in Partial Differential Equations. (In Press)

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Abstract

Let (Formula presented.) denote Euclidean n space and given k a positive integer let (Formula presented.) be a k-dimensional plane with (Formula presented.) If (Formula presented.) we first study the Martin boundary problem for solutions to the p-Laplace equation (called p-harmonic functions) in (Formula presented.) relative to (Formula presented.) 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 (Formula presented.) to p-harmonic functions in (Formula presented.) when (Formula presented.) Finally, we discuss generalizations of our work to solutions of p-Laplace type PDE (called (Formula presented.) -harmonic functions).

Item Type: Monograph (Working Paper)
Additional Information: 47 Pages
Uncontrolled Keywords: math.AP; 35J60, 31B15, 39B62, 52A40, 35J20, 52A20, 35J92
Divisions: Faculty of Science and Health
Faculty of Science and Health > Mathematical Sciences, Department of
SWORD Depositor: Elements
Depositing User: Elements
Date Deposited: 16 Sep 2021 10:10
Last Modified: 15 Jul 2022 21:32
URI: http://repository.essex.ac.uk/id/eprint/31102

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