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arXiv · 2307.12124

$p-$Harmonic functions in the upper half-space

Emerson Abreu·Rodrigo Clemente·João Marcos Do Ó·Everaldo Medeiros
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Abstract

This paper investigates the existence, nonexistence, and qualitative properties of p-harmonic functions in the upper half-space $\mathbb{R}^N_+ \, (N \geq 3)$ satisfying nonlinear boundary conditions for $1<p<N$. Moreover, the symmetry of positive solutions is shown by using the method of moving planes.

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Emerson Abreu, Rodrigo Clemente, João Marcos Do Ó, Everaldo Medeiros. 2023-07-22. $p-$Harmonic functions in the upper half-space. https://arxiv.org/abs/2307.12124

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