Symmetry via antisymmetric maximum principles in nonlocal problems of variable order (Q5964961)

The authors study nonlinear problems of the type \(Iu=f(x,u)\) in \(\Omega\), \(u=0\) on \(\mathbb R^N\setminus\Omega\), for open bounded \(\Omega\). Here \(I\) is nonlocal, e.g. a fractional Laplacian, and of varying order. Under structural assumptions on \(I\), \(\Omega\) and \(f\) with respect to a fixed direction \(\xi\) they prove Steiner symmetry of solutions with a new variant of the maximum principle.