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arXiv · 2607.00617

Monotonicity of non-negative solutions of quasilinear elliptic equations in a cylindrical domain

Luigi Montoro·Luigi Muglia·Berardino Sciunzi·Giuseppe Spadaro
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Abstract

We consider weak solutions to $p$-Laplace equations in cylindrical domains under mixed homogeneous Dirichlet-Neumann boundary conditions. We assume that the right-hand side is positive and locally Lipschitz continuous and we prove that any positive solution is monotone increasing in the $x_N$ direction for any $p>1$. As an application we prove that solutions to Allen-Cahn type equations are one-dimensional as well as a Liouville type result for Lane-Emden type equations.

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Luigi Montoro, Luigi Muglia, Berardino Sciunzi, Giuseppe Spadaro. 2026-07-01. Monotonicity of non-negative solutions of quasilinear elliptic equations in a cylindrical domain. https://arxiv.org/abs/2607.00617

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