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math.AP2025
Fractional De Giorgi conjecture in dimension 2 via complex-plane methods
Serena Dipierro, João Gonçalves da Silva, Giorgio Poggesi +1
We provide a new proof of the fractional version of the De Giorgi conjecture for the Allen-Cahn equation in for the full range of exponents. Our proof combines a met…
math.AP2024
A quantitative Gidas-Ni-Nirenberg-type result for the -Laplacian via integral identities
Serena Dipierro, João Gonçalves da Silva, Giorgio Poggesi +1
We prove a quantitative version of a Gidas-Ni-Nirenberg-type symmetry result involving the -Laplacian. Quantitative stability is achieved here via integral identities based on t…
math.AP2024
A general integral identity with applications to a reverse Serrin problem
Rolando Magnanini, Riccardo Molinarolo, Giorgio Poggesi
We prove a new general differential identity and an associated integral identity, which entails a pair of solutions of the Poisson equation with constant source term. This generali…