4 papers · 1 filter
Some Fractional Functional Inequalities and Applications to Some Constrained Minimization Problems Involving a Local Non-linearity
Hichem Hajaiej
In this paper we prove the Fractional Gagliardo-Nirenberg Inequality, Polya-Szego Inequality and the Sharp Fractional Sobolev Inequality, we then provide an application of such ine…
Symmetric Ground States Solutions of M-Coupled Nonlinear Schrodinger Equations
Hichem Hajaiej
We prove the existence of radial and radially decreasing ground states of an m-coupled nonlinear Schrodinger equation with a general nonlinearity.
Balls are Maximizers of the Riesz-Type Functionals with Supermodular Integrands
Hichem Hajaiej
For a large class of supermodular integrands, we establish conditions under which balls are the unique (up to translations) maximizers of the Riesz-type functionals with constraint…
Rearrangement inequalities for functionals with monotone integrands
Almut Burchard, Hichem Hajaiej
The rearrangement inequalities of Hardy-Littlewood and Riesz say that certain integrals involving products of two or three functions increase under symmetric decreasing rearrangeme…