On Concavity of Solutions of the Nonlinear Poisson Equation

Concavity of solutions to semilinear equations in dimension two

“…This extends a recent result of Steinerberger [20], who proved the same result under additional assumptions on 𝑓 ′ . Earlier work of established it for the torsion problem.…”

“…Recently Steinerberger [20] asked: Question Under what conditions on $$f$$ and $$\Omega$$ is the function $$u$$ concave on $$\Omega$$?…”