Regularity for C^{1,\alpha} interface transmission problems

Transmission problems originally arose in elasticity theory, and they are nowadays of great interest due to their many applications in different areas in science. Typically, in these problems, there is a fixed interface where solutions may change abruptly, and the primary focus is to study their behavior across this surface. In this talk, we will

Regularity Estimate for Nonlocal Space-Time Master Equations

We analyze regularity estimates for solutions to nonlocal space-time equations driven by fractional powers of parabolic operators in divergence form. These equations are fundamental in semipermeable membrane problems, biological invasion models and they also appear as generalized Master equations. We develop a parabolic method of semigroups that allows us to prove a local extension problem

Instability of Finite Time Blow-up For Incompressible Euler

In this talk, we will discuss the interaction between the stability, and the propagation of regularity, for solutions to the incompressible 3D Euler equation. It is still unknown whether a solution with smooth initial data can develop a singularity in finite time. We will describe how, in such a scenario, the solution becomes unstable as

Boundedness Properties for Hermite Pseudo-Multipliers

Fourier multipliers and pseudo-differential operators are defined by means of the Fourier transform and play an important role in the study of partial differential equations. In the same spirit, Hermite pseudo-multipliers are associated to Hermite expansions and they represent the counterparts to pseudo-differential operators in the Hermite setting. After some preliminaries, we will present results