August 6, 2025

Hardy-type inequalities for the drifting p-Laplace operator and applications

Puntos clave

The study derives generalized weighted hardy-type inequalities for the drifting p-laplace operator.
It establishes Liouville-type results for positive solutions of elliptic problems with singular lower order terms.
The mathematical analysis involves both bounded and unbounded domains in higher dimensions.
Findings advance understanding of nonsingular quasilinear elliptic problems with various weights.

Resumen

Abstract We consider the drifting p -Laplace operator equation* ₏, ₕu=e^-v div\, (eᵛ | u|^p-2 u) equation* and discuss generalized weighted Hardy-type inequalities associated with the measure d=e^v (x) dx. As an application, we obtain several Liouville-type results for positive solutions of the non-linear elliptic problem with singular lower order term equation*-₏, ₕ u c (x) u^p-1+B | u|ᵖu in\, equation* where Ω is a bounded or an unbounded exterior domain in RN, N p 1, B+p-1 0, as well as of the non-autonomous quasilinear elliptic problem equation*-₏, ₕ u+b (x) | u|^p-1 c (x) u^p-1 in\, equation* with general weights b0 and c > 0. Liouville-type results are also discussed for a class of higher order differential equations.

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