We investigate the validity of Gaussian lower bounds for solutions to an electromagnetic Schrödinger equation with a bounded time-dependent complex electric potential and time-independent vector magnetic potential. prove that, if suitable geometric condition is satisfied by potential, then positive masses inside region at single time propagate outside region, provided average in space–time cyli...

Given an evolution equation, a standard way to prove the well posedness of the Cauchy problem is to establish a Gronwall type estimate, bounding the distance between any two trajectories. There are important cases, however, where such estimates cannot hold, in the usual distance determined by the Euclidean norm or by a Banach space norm. In alternative, one can construct different distance func...

we mean an equivalence class of paths modulo reparametrizations. Write CD for the set of chords in D. Given a path γ, we write [γ] for the associated chord; more generally, if γ is a continuous map from any compact subinterval I of [0,∞] to Û , starting at z0 and ending at z1, we can obtain a chord [γ] in D by choosing an increasing homeomorphism φ : [0, 1] → I and setting [γ] = [γ ◦ φ]. Write ...