5 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 esta…
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 $(-Î…
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…
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…