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Factorizations and Hardy-Rellich inequalities on stratified groups
In this paper, we obtain Hardy, Hardy-Rellich and refined Hardy inequalities on general stratified groups and weighted Hardy inequalities on general homogeneous groups using the factorization method of differential operators, ...
Critical Gagliardo-Nirenberg, Trudinger, Brezis-Gallouet-Wainger inequalities on graded groups and ground states
In this paper we investigate critical Gagliardo-Nirenberg, Trudinger-type and Brezis-Gallouet-Wainger inequalities associated with the positive Rockland operators on graded groups, which includes the cases of $\mathbb R^n$, ...
A comparison principle for higher order nonlinear hypoelliptic heat operators on graded Lie groups
(2021)
In this paper we present a comparison principle for higher order nonlinear hypoelliptic heat operators on graded Lie groups. Moreover, using the comparison principle we obtain blow-up type results and global in $t$-boundedness ...
Existence and non-existence of global solutions for semilinear heat equations and inequalities on sub-Riemannian manifolds, and Fujita exponent on unimodular Lie groups
(Elsevier, 2021)
In this paper we study the global well-posedness of the following Cauchy problem on a sub-Riemannian manifold $M$: \begin{equation*} \begin{cases} u_{t}-\mathfrak{L}_{M} u=f(u), \;x\in M, \;t>0, \\u(0,x)=u_{0}(x), \;x\in ...
Hardy, weighted Trudinger-Moser and Caffarelli-Kohn-Nirenberg type inequalities on Riemannian manifolds with negative curvature
(Elsevier, 2021-10)
In this paper we obtain Hardy, weighted Trudinger-Moser and Caffarelli-Kohn-Nirenberg type inequalities with sharp constants on Riemannian manifolds with non-positive sectional curvature and, in particular, a variety of ...
Very weak solutions to hypoelliptic wave equations
(2020-02-15)