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math.AP2015
The Matzoh Ball Soup Problem: a complete characterization
Rolando Magnanini, Michele Marini
We characterize all the solutions of the heat equation that have their (spatial) equipotential surfaces which do not vary with the time. Such solutions are either isoparametric or…
math.AP2015★ 3 cited
Symmetry and linear stability in Serrin's overdetermined problem via the stability of the parallel surface problem
Giulio Ciraolo, Rolando Magnanini, Vincenzo Vespri
We consider the solution of the problem $$ -Δu=f(u) \ \mbox{ and } \ u>0 \ \ \mbox{ in } \ Ω, \ \ u=0 \ \mbox{ on } \ Γ, $$ where is a bounded domain in with bou…