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Nonexistence results for parabolic equations involving the p-Laplacian and Hardy–Leray-type inequalities on Riemannian manifolds
(Birkhauser, 2021) Goldstein, G.R.; Goldstein, J.A.; Kömbe, İsmail; Bakım, Sümeyye
The main goal of this paper is twofold. The first one is to investigate the nonexistence of positive solutions for the following nonlinear parabolic partial differential equation on a noncompact Riemannian manifold M
A unified approach to weighted Hardy type inequalities on Carnot groups
(Southwest Missouri State University, 2017) Goldstein, J.A.; Kömbe, İsmail; Yener, Abdullah
We find a simple sufficient criterion on a pair of nonnegative weight functions V (x) and W (x) on a Carnot group G; so that the general weighted Lp Hardy type inequality (Equation presentted) is valid for any ? ? C? 0 (G) and p > 1: It is worth noting here that our unifying method may be readily used both to recover most of the previously known weighted Hardy and Heisenberg-Pauli-Weyl type inequalities as well as to construct other new inequalities with an explicit best constant on G: We also present some new results on two-weight Lp Hardy type inequalities with remainder terms on a bounded domain ? in G via a differential inequality.