Serena Federico, Alma Mater Università di Bologna

https://sites.google.com/site/serenafederico3/

Dicember 9th, 2025. 

Time: 5 PM 

Where: Seminario 1 (Dip. Mat. UNIBO)

Abstract:  In this talk, I will give a brief introduction to Carleman estimates and show their application to some problems in PDEs, such as, for instance, the uniqueness of solutions and the local solvability.

Gabriele Giannone, University of Florence

https://www.researchgate.net/profile/Gabriele-Giannone-2

Dicember 16th, 2025. 

Time: 5 PM 

Where: Seminario 1 (Dip. Mat. UNIBO)

Abstract:  One of the most basic and important questions in PDE is that of regularity. It is also a unifying problem in the field, since it affects all kinds of PDEs. A classical example is Hilbert’s XIXth problem (1900), which roughly speaking asked to determine whether all solutions to uniformly elliptic variational PDEs are smooth. Starting from De Giorgi’s groundbreaking approach to this problem (1957), the first part of this talk will review the core ideas of elliptic regularity theory, emphasizing the main differences between the linear and nonlinear settings. We will then turn to the more recent theory of elliptic PDEs with p,q-growth - that is, elliptic equations whose ellipticity and growth are governed by different powers of the gradient. In this setting, a central feature is that regularity does not always hold: as shown by counterexamples due to Marcellini (1987) and Giaquinta (1987), certain variational integrals admit unbounded minimizers as soon as p and q are too far apart. Ensuring regularity for all solutions therefore requires an appropriate balance between p and q. Finally, we will discuss some current developments in which the growth of the stress field is prescribed by distinct Young functions, leading to an Orlicz-type framework that captures a broad range of nonstandard behaviors and provides a natural setting for genuinely non-homogeneous problems.

Laura Baldelli, Karlsruhe Institute of Technology (KIT)

https://laurabaldelli.mobirisesite.com/

Dicember 18th, 2025. 

Time: 3 PM 

Where: Seminario 1 (Dip. Mat. UNIBO)

Abstract:  This talk focuses on a family of Hardy-Sobolev doubly critical p-Laplace systems defined on the whole Euclidean space. A key tool in our analysis is the moving plane method, which will serve as our starting point. We will outline the origins of this method, explain its main features, and discuss the current state of the art in the context of more general problems, culminating in the system under consideration. Particular attention will be paid to how the nonlinear nature of the operator, the presence of Hardy’s potential, and the coupled structure of the system make the application of the method highly nontrivial. 

Francesca De Giovanni, University of Naples Federico II

https://www.researchgate.net/profile/Francesca-De-Giovanni-2

February 24th, 2025. 

Time: 5 PM 

Where: Seminario 1 (Dip. Mat. UNIBO)

Abstract:  TBA