35 citations · 108 across the 18 of their papers we have counts for
18 papers
Sharp -regularity in dimensions and beyond for two classes of elliptic problems with critical unbounded coefficients
Cristian Cazacu, Adelina Călina
We establish sharp parameter thresholds governing -regularity of weak solutions in for two classes of elliptic problems with critical unbounded perturbations, in dime…
Sharp second order inequalities with distance function to the boundary and applications to a p-Biharmonic singular problem
Cristian Cazacu, Teodor Rugină
In this paper, we prove generalizations to the L^p setting of the Hardy-Rellich inequalities on domains of R^N with singularity given by the distance function to the boundary. The…
Weighted Hardy-Rellich type inequalities: improved best constants and symmetry breaking
Cristian Cazacu, Irina Fidel
When studying the weighted Hardy-Rellich inequality in with the full gradient replaced by the radial derivative the best constant becomes trivially larger or equal than in th…
Caffarelli-Kohn-Nirenberg identities, inequalities and their stabilities
Cristian Cazacu, Joshua Flynn, Nguyen Lam +1
We set up a one-parameter family of inequalities that contains both the Hardy inequalities (when the parameter is 1) and the Caffarelli-Kohn-Nirenberg inequalities (when the parame…
Best constants in bipolar L^p-Hardy-type Inequalities
Cristian Cazacu, Teodor Rugină
In this work we prove sharp versions of multipolar Hardy inequalities in the case of a bipolar potential and , which were first developed in the case by Cazacu…
The Hardy inequality and large time behaviour of the heat equation on
Cristian Cazacu, Liviu I. Ignat, Dragoş Manea
In this paper we study the large time asymptotic behaviour of the heat equation with Hardy inverse-square potential on corner spaces , $k\geq 0…
Hardy inequalities for magnetic -Laplacians
Cristian Cazacu, David Krejcirik, Nguyen Lam +1
We establish improved Hardy inequalities for the magnetic -Laplacian due to adding nontrivial magnetic fields. We also prove that for Aharonov-Bohm magnetic fields the sharp con…
Caffarelli-Kohn-Nirenberg inequalities for curl-free vector fields and second order derivatives
Cristian Cazacu, Joshua Flynn, Nguyen Lam
The present work has as a first goal to extend the previous results in \cite{CFL20} to weighted uncertainty principles with nontrivial radially symmetric weights applied to curl-fr…
Short proofs of refined sharp Caffarelli-Kohn-Nirenberg inequalities
Cristian Cazacu, Joshua Flynn, Nguyen Lam
This note relies mainly on a refined version of the main results of the paper by F. Catrina and D. Costa (J. Differential Equations 2009). We provide very short and self-contained…
Sharp second order uncertainty principles
Cristian Cazacu, Joshua Flynn, Nguyen Lam
We study sharp second order inequalities of Caffarelli-Kohn-Nirenberg type in the euclidian space , where denotes the dimension. This analysis is equivalent to…
The method of super-solutions in Hardy and Rellich type inequalities in the setting: an overview of well-known results and short proofs
Cristian Cazacu
In this survey we give a compact presentation of well-known functional inequalities of Hardy and Rellich type in the setting. In addition, we give some insights of their proo…
Hardy inequalities for inverse square potentials with countable number of singularities
Cristian Cazacu, Aurora Marica
The Hardy Inequality (HI) for potentials with countably many singularities of the form is not a trivial issue. In principle, the more…
A new proof of the Hardy-Rellich inequality in any dimension
Cristian Cazacu
The Hardy-Rellich inequality in the whole space with the best constant was firstly proved by Tertikas and Zographopoulos in Adv. Math. (2007) in higher dimensions . Then i…
New estimates for the Hardy constants of multipolar Schrödinger operators
Cristian Cazacu
In this paper we study the optimization problem $$μ^\star(Ω):=\inf_{u\in \semi}\frac{\into |\n u|^2 \dx}{\into V u^2 \dx}$$ in a suitable functional space $\semi$. Here, is the…
Schrödinger operators with boundary singularities: Hardy inequality, Pohozaev identity and controllability results
Cristian Cazacu
The aim of this paper is two folded. Firstly, we study the validity of the Pohozaev-type identity for the Schrödinger operator $$A_\la:=-\D -\frac{\la}{|x|^2}, \q \la\in \rr,$$ in…
Hardy inequality and Pohozaev identity for operators with boundary singularities: some applications
Cristian Cazacu
We consider the Schrödinger operator $A_ł:=-\D -ł/|x|^2$, $ł\in \rr$, when the singularity is located on the boundary of a smooth domain $Ω\subset \rr^N$, The aim of this…
Hardy inequalities with boundary singularities
Cristian Cazacu
In this work we prove some Hardy-Poincaré inequalities with quadratic singular potentials localized on the boundary of a smooth domain. Then, we consider conical domains with verte…
Twisted sums, Fenchel-Orlicz spaces and property (M)
George Androulakis, C. D. Cazacu, Nigel J. Kalton
We study certain twisted sums of Orlicz spaces with non-trivial type which can be viewed as Fenchel-Orlicz spaces on . We then show that a large class of Fenchel-O…