Monotonicity of solutions of quasilinear degenerate elliptic equation in half-spaces

By Alberto Farina, Luigi Montoro, Berardino Sciunzi. 2012

47 citations recorded by the source corpus.

We prove a weak comparison principle in narrow unbounded domains for solutions to $$-\Delta _p u=f(u)$$ in the case $$2<p< 3$$ and $$f(\cdot )$$ is a power-type nonlinearity, or in the case $$p>2$$ and $$f(\cdot )$$ is super-linear. We exploit it to prove the monotonicity of positive solutions to $$-\Delta _p u=f(u)$$ in half spaces (with zero Dirichlet assumption) and therefore to prove some Liouville-type theorems.

Subfields: Applied Mathematics, Computational Theory and Mathematics

View Paper: https://www.semanticscholar.org/paper/bc736e56600b8929a7eba47f1604dd62277e2362

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In Applied Mathematics

In Computational Theory and Mathematics

Citations in the corpus

Radial symmetry and applications for a problem involving the $-\Delta_p(\cdot)$ operator and critical nonlinearity in~$\mathbb{R}^N$ (2014, background): “The problem in half spaces has been studied in [12, 16, 17].”