Domínguez Vázquez, MiguelEnciso, AlbertoPeralta-Salas, Daniel2024-10-042024-10-042019Adv. Math. 351 (2019), 718-760http://hdl.handle.net/10347/35011We show that a wide range of overdetermined boundary problems for semilinear equations with position-dependent nonlinearities admits nontrivial solutions. The result holds true both on R^n and on compact Riemannian manifolds. As a byproduct of the proofs we also obtain some rigidity, or partial symmetry, results for solutions to overdetermined problems on Riemannian manifolds of nonconstant curvature.engCC BY-NC-NDOverdetermined boundary value problemsSemilinear elliptic problemsAsymptotically homogeneous spacesSymmetric spacesHarmonic spacesjournal article10.1016/j.aim.2019.05.017open access