Alberto Farina

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math.AP2025

One-dimensional symmetry results for semilinear equations and inequalities on half-spaces

Nicolas Beuvin, Alberto Farina

We prove new one-dimensional symmetry results for non-negative solutions, possibly unbounded, to the semilinear equation $- Δ u = f (u)$ in the upper half-space $R_{+}^{N}$ .…

math.AP2025

Monotonicity for solutions to semilinear problems in epigraphs

Nicolas Beuvin, Alberto Farina, Berardino Sciunzi

We consider positive solutions, possibly unbounded, to the semilinear equation $- Δ u = f (u)$ on continuous epigraphs bounded from below. Under the homogeneous Dirichlet boundary condi…