## 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).

Original language | English (US) |
---|---|

Pages (from-to) | 1457-1503 |

Number of pages | 47 |

Journal | Communications in Partial Differential Equations |

Volume | 47 |

Issue number | 7 |

DOIs | |

State | Published - 2022 |

## Keywords

- Fatou theorem
- Gap series
- p-harmonic function
- p-harmonic measure
- radial limits

## ASJC Scopus subject areas

- Analysis
- Applied Mathematics