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math.AP2025
Ground-state blowing-up solutions for a Hardy-Sobolev equations on a manifold
Hussein Cheikh Ali, Frédéric Robert
We prove the existence of blowing-up families of solutions to an equation of Hardy-Sobolev type in high dimensions. These families are of minimal type. The sole condition is that t…
math.AP2024
Critical dimensions for polyharmonic operators: The Pucci-Serrin conjecture for solutions of bounded energy
Frédéric Robert
We prove a Pucci-Serrin conjecture on critical dimensions under a uniform bound on the energy. The method is based on the analysis of the Green's function of polyharmonic operators…