## Abstract

We consider existence and uniqueness of homogeneous solutions u> 0 to certain PDE of p-Laplace type, p fixed, n- 1 < p< ∞, n≥ 2 , when u is a solution in K(α) ⊂ R^{n} where K(α):={x=(x1,⋯,xn):x1>cosα|x|}forfixedα∈(0,π],with continuous boundary value zero on ∂K(α) \ { 0 }. In our main result we show that if u has continuous boundary value 0 on ∂K(π) then u is homogeneous of degree 1 - (n- 1) / p when p> n- 1. Applications of this result are given to a Minkowski type regularity problem in R^{n} when n= 2 , 3.

Original language | English (US) |
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Article number | 47 |

Journal | Calculus of Variations and Partial Differential Equations |

Volume | 59 |

Issue number | 2 |

DOIs | |

State | Published - Apr 1 2020 |

## ASJC Scopus subject areas

- Analysis
- Applied Mathematics

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