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math.AP2026
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…
math.AP2026
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…
math.AP2026
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…