1 citations · 2 across the 10 of their papers we have counts for
11 papers
A Lions' type formula for some reproducing kernel Hilbert spaces of fractional harmonic functions
Sidy M. Djitte, Franck Sueur
In \cite{Lions}, J. L. Lions considered a reproducing kernel Hilbert space (RKHS) of harmonic functions on a regular domain with Sobolev traces and obtained a formula that expresse…
A Brezis and Peletier type result for the fractional Robin function
Sidy M. Djitte, Franck Sueur
This paper is devoted to the Laplacian operator of fractional order in several dimensions. We consider the equation in , in and establi…
Pointwise Hadamard variational formula for the fractional Laplacian
Sidy M. Djitte, Franck Sueur
We establish pointwise formulas for the shape derivative of solutions to the Dirichlet problem associated with the fractional Laplacian. Specifically, we consider the equation $(-Δ…
Pohozaev-like identity for the regional fractional laplacian
Sidy M. Djitte
We establish a new integration by parts formula for the regional fractional laplacian in bounded open sets of class . As a direct application, we prove that weak so…
Shape derivative approach to fractional overdetermined problems
Sidy M. Djitte, Ignace A. Minlend
We use shape derivative approach to prove that balls are the only convex and regular domains in which the fractional overdetermined problem \begin{equation*} \left\{\begi…
A few representation formulas for solutions of fractional Laplace equations
Sidy M. Djitte, Franck Sueur
This paper is devoted to the Laplacian operator of fractional order in several dimensions. We first establish a representation formula for the partial derivatives of t…
Fractional Hardy-Rellich inequalities via integration by parts
Nicola De Nitti, Sidy Moctar Djitte
We prove a fractional Hardy-Rellich inequality with an explicit constant in bounded domains of class . The strategy of the proof generalizes an approach pioneered by E. Mi…
Nonradiality of second fractional eigenfunctions of thin annuli
Sidy M. Djitte, Sven Jarohs
In the present paper, we study properties of the second Dirichlet eigenvalue of the fractional Laplacian of annuli-like domains and the corresponding eigenfunctions. In the first p…
A generalized fractional Pohozaev identity and applications
Sidy Moctar Djitte, Mouhamed Moustpha Fall, Tobias Weth
We prove a fractional Pohozaev type identity in a generalized framework and discuss its applications. Specifically, we shall consider applications to nonexistence of solutions in t…
Symmetry of odd solutions to equations with fractional Laplacian
Sidy M. Djitte, Sven Jarohs
We present a symmetry result to solutions of equations involving the fractional Laplacian in a domain with at least two perpendicular symmetries. We show that if the solution is co…
A fractional Hadamard formula and applications
Sidy Moctar Djitte, Mouhamed Moustapha Fall, Tobias Weth
We consider the domain dependence of the best constant in the subcritical fractional Sobolev constant, $$ λ_{s,p}(Ω):=\inf \left\{ [u]_{H^s(\mathbb{R}^N)}^2,\,\, u\in C^\infty_c(Ω)…