Title and Abstract

14th, 14:30 - 15:30

On pointwise convergence to the heat equations

We completely characterize the weighted Lebesgue spaces on torus for which the solutions of the heat equation converge pointwise (as time tends to zero) to the initial data. Then we shall formulate conditions to generalize this result for the abstract heat equation in the setting of metric measure spaces. We shall highlight that our generic result can cover: Laplacian in the presence of Hardy potential, Dunkle Laplacian, Laplacian on Riemannian manifold etc.

We shall also mention some recent progress in this direction  for modulation spaces.