D. W. Robinson

activity

19962021

most citedDegenerate elliptic operators: capacity, flux and separation

12 citations · 50 across the 28 of their papers we have counts for

collaborators

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21 papers · 1 filter

math.AP2021★ 1 cited

The weighted Hardy constant

Derek W. Robinson

Let $Ω$ be a domain in $R^{d}$ and $d_{Γ}$ the Euclidean distance to the boundary $Γ$ . We investigate whether the weighted Hardy inequality \[ \|d_Γ^{δ/2-1}φ\|_2\leq a_δ\,\|d_Γ^{δ/2}\,…

math.AP2017★ 5 cited

Hardy and Rellich inequalities on the complement of convex sets

Derek W. Robinson

We establish existence of weighted Hardy and Rellich inequalities on the spaces $L_{p} (Ω)$ where $Ω= \Ri^d\backslash K$ with $K$ a closed convex subset of $\Ri^d$. Let $Γ = \partial Ω$ …

math.AP2017★ 1 cited

Hardy inequalities, Rellich inequalities and local Dirichlet forms

Derek W. Robinson

First the Hardy and Rellich inequalities are defined for the submarkovian operator associated with a local Dirichlet form. Secondly, two general conditions are derived which are su…

math.AP2015★ 7 cited

Uniqueness of diffusion on domains with rough boundaries

Juha Lehrbäck, Derek W. Robinson

Let $Ω$ be a domain in $R^{d}$ and $h (φ) = \sum_{k, l = 1}^{d} (\partial_{k} φ, c_{k l} \partial_{l} φ)$ a quadratic form on $L_{2} (Ω)$ with domain $C_{c}^{\infty} (Ω)$ where the $c_{k l}$ are real…

math.AP2014

Grušin operators, Riesz transforms and nilpotent Lie groups

Derek W Robinson, Adam Sikora

We establish that the Riesz transforms of all orders corresponding to the Grušin operator $H_{N} = - \nabla_{x}^{2} - ∣ x ∣^{2 N} \nabla_{y}^{2}$ , and the first-order operators $(\nabla_{x},x^ν…

math.AP2013

Uniqueness of diffusion operators and capacity estimates

Derek W Robinson

Let $Ω$ be a connected open subset of $\Ri^d$. We analyze $L_{1}$ -uniqueness of real second-order partial differential operators $H = - \sum_{k, l = 1}^{d} \partial_{k} c_{k l} \partial_{l}$ and…