13h30-14h30 | Online (pw: lisbonwade)

• Mateus Costa de Sousa (Basque Center for Applied Mathematics)
• Sharp embeddings between weighted Paley–Wiener spaces
  • In this talk we will discuss some extremal problems related to embeddings between weighted Paley–Wiener spaces. We will present some asymptotic results for sharp constants in terms of the parameters involved, deduce existence results for extremal functions as well as radial symmetry of those, and talk about some numerical results. For certain cases, these extremal problems can be reformulated in terms of sharp Poincaré inequalities, and for those cases we will present a characterisation of extremizers and sharp constants that recover several classical results.

14h30-15h30 | Online (pw: lisbonwade)

• Héctor Chang Lara, (CIMAT, Mexico)
• A transmission problem for first and second order operators
  • We establish the existence and uniqueness of viscosity solutions within a domain $\Omega\subseteq \mathbb{R}^n$ for a class of equations governed by elliptic and eikonal type equations in disjoint regions. Our primary motivation stems from the Hamilton-Jacobi equation that arises in the context of a stochastic optimal control problem.

The Lisbon Webinar in Analysis in Differential Equations is a joint iniciative of CAMGSD, CMAFcIO and GFM, three research centers of the University of Lisbon. It is aimed at filling the absence of face-to-face seminars and wishes to be a meeting point of mathematicians working in the field.