Monotonicity results in half spaces for quasilinear elliptic equations involving a singular term

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2025年9月25日

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Luigi Montoro,
Luigi Muglia,
Berardino Sciunzi

摘要

We consider positive solutions to $\displaystyle -\Delta _p u=\frac{1}{u^\gamma }+f(u)$ $- Δ_{p} u = \frac{1}{u^{γ}} + f (u)$ under zero Dirichlet condition in the half space. Exploiting apriori estimates and the moving plane technique, we prove that any solution is monotone increasing in the direction orthogonal to the boundary.