Local Bernstein inequalities for eigenfunctions
Stefano Decio, Eugenia Malinnikova · Advances in Mathematics · 2025
Let be an eigenfunction of the Laplace-Beltrami operator on a smooth compact Riemannian manifold, meaning that . We show that satisfies a local Bernstein inequality; namely for any geodesic ball and any the following inequality holds: . We also prove analogous inequalities for solutions of elliptic PDEs in terms of the frequency function.