Philippe Souplet

Sharp gradient bounds for uniformly elliptic PDE, eigenvalue asymptotics, and the Landis conjecture

We study three classical problems in the theory of linear second-order uniformly elliptic equations: (i) gradient estimates for the Dirichlet problem, (ii) estimates and asymptotics for the first eigenvalue of an elliptic operator, and (iii) the Landis conjecture on exponential decay. Our main results give versions of...