Titles and Abstracts

The subject of the talk are well-posedeness and (maximal) regularity properties of elliptic operators and the corresponding evolution equation with minimal hypotheses on coefficients and domains. One ingredient of the talk is the article: W.Arendt, R. Schätzle: Semigroups generated by elliptic operators in non-divergence form on unbounded domains. Ann. Scuola Norm. , to appear.

The subject of the talk are well-posedeness and (maximal) regularity properties of elliptic operators and the corresponding evolution equation with minimal hypotheses on coefficients and domains. One ingredient of the talk is the article: W.Arendt, R. Schätzle: Semigroups generated by elliptic operators in non-divergence form on unbounded domains. Ann. Scuola Norm. , to appear.

We extend the concept of p-ellipticity for scalar elliptic operators to the case of elliptic systems with complex coefficients. Although our condition turns out to be equivalent to a condition for systems (equally named) by Dindoš, Li and Pipher (2021), the two approaches are different and yield different results. This is a joint work with Oliver Dragičević

This is a join work with Baldi, Cupini, Galeotti. We introduce a conformal version of the Laplacian on the plane and prove that a power of the distance is a parametrix of its fundamental solution. 

As a consequence, we obtain a representation formula for smooth functions in terms of the gradient of the function and the gradient of the approximated fundamental solution.

In this talk we study inverse problems involving a fractional time derivative of Caputo type of order $\alpha\in(0,1)$.

Firstly, we consider a fractional-in-time inverse problem $(P)$ modeling anisotropic subdiffusion. We prove the uniqueness of the solution of the inverse problem under suitable additional conditions and we provide a conditioned existence result.

Secondly, we investigate the "asymptotics" of the solution of the above inverse problem. More precisely, we study approximating time-fractional inverse problems $(P_n)$, for $n\in\mathbb{N}$, and we prove that the sequence of solutions of these approximating problems converges (in a suitable weak sense) to the solution of the inverse problem $(P)$.

We then present some applications to boundary value problems (possibly in irregular domains).

These results are obtained in collaboration with M. R. Lancia (Sapienza), A. Mola (IMT Lucca), G. Mola (Sorbonne Abu Dhabi) and S. Romanelli (Bari).

Aim of this seminar is to illustrate to an audience with a basic understanding of functional analysis a quite famous result which is generally known as the "Dore-Venni theorem"

In this talk, I will present some results on non-local equations, possibly on domains with fractal boundaries, where the non-locality can arise from the presence of non-local operators in space or non-local operators in time. In particular, the operators under consideration are not only generators of suitable Dirichlet forms, but can also be the square of a suitable first-order operator. We will present well-posedness results, as well as discuss limit behaviors and open problems.

In this talk, I will present a survey of classical and recent results on the characterization of Euclidean balls via volume and surface mean value formulas for harmonic functions.

In this talk, elliptic systems of second order with unbounded coefficients in R^d are considered. In particular, problems depending on a complex parameter are treated. The results are employed to study corresponding parabolic systems.