4 papers · 1 filter
Fujita exponent for heat equation with Hörmander vector fields
Marianna Chatzakou, Aidyn Kassymov, Michael Ruzhansky
In this paper, we show global existence and non-existence results for the heat equation with some of the squares of smooth vector fields on $\Rn$ satisfying Hörmander's rank condi…
Berezin-Li-Yau inequality for mixed local-nonlocal Dirichlet-Laplacian
Aidyn Kassymov, Berikbol T. Torebek
In this paper, we consider an eigenvalue problem for mixed local-nonlocal Laplacian $$\mathcal{L}^{a,b}_{\Om}:=-aÎ+b(-Î)^s,\,a>0,\,b\in\mathbb{R},\,s\in (0,1),$$ with Dirichlet b…
Fractional Hardy type inequalities on homogeneous Lie groups in the case
Aidyn Kassymov, Michael Ruzhansky, Durvudkhan Suragan
In this paper, we obtain a fractional Hardy inequality in the case on homogeneous Lie groups, and as an application we show the corresponding uncertainty principle. Also, we…
On fractional inequalities on metric measure spaces with polar decomposition
Aidyn Kassymov, Michael Ruzhansky, Gulnur Zaur
In this paper, we prove the fractional Hardy inequality on polarisable metric measure spaces. The integral Hardy inequality for is playing a key role in the proo…