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math.AP2025
On stable solutions to the Allen-Cahn equation with bounded energy density in
Enric Florit-Simon, Joaquim Serra
We show that stable solutions to the Allen-Cahn equation with bounded energy density (or equivalently, with cubic energy growth) are one-dimensional. Thi…
math.AP2016★ 1 cited
The boundary Harnack principle for nonlocal elliptic operators in non-divergence form
Xavier Ros-Oton, Joaquim Serra
We prove a boundary Harnack inequality for nonlocal elliptic operators in non-divergence form with bounded measurable coefficients. Namely, our main result establishes that if…
math.AP2012
Fractional Laplacian: Pohozaev identity and nonexistence results
Xavier Ros-Oton, Joaquim Serra
In this note we present the Pohozaev identity for the fractional Laplacian. As a consequence of this identity, we prove the nonexistence of nontrivial bounded solutions to semiline…