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The Hardy inequality and Nonlinear parabolic equations on Carnot groups

Ismail Kombe
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Abstract

In this paper we shall investigate the nonexistence of positive solutions for the following nonlinear parabolic partial differential equation:\[ \begin{cases} \frac{\partial u}{\partial t}= Δ_{\mathbb{G},p}u+V(x)u^{p-1} & \text{in}\quad Ω\times (0, T), \quad 1<p<2, u(x,0)=u_{0}(x)\geq 0 & \text{in} \quadΩ, u(x,t)=0 & \text{on}\quad \partialΩ\times (0, T) \end{cases} \] where $ Δ_{\mathbb{G},p}$ is the $p$-sub-Laplacian on Carnot group $ \mathbb{G}$ and $V\in L_{\text{loc}}^1(Ω)$.

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Ismail Kombe. 2005-04-04. The Hardy inequality and Nonlinear parabolic equations on Carnot groups. https://arxiv.org/abs/math/0504057

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