Overview
We present a school aimed to promote the topic of evolutionary problems modelled by partial differential equations and gather the young research community in PDEs. Apart from courses, we plan to enhance the visibility of PhD students and early-stage researchers by organizing a special session enabling them to share their results.
Lecturers
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- Massimiliano Morini (Università degli Studi di Parma, Italy)
TBA
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- Xavier Ros Oton (Universitat de Barcelona, Spain)
Stable solutions to nonlinear elliptic PDE
We study stable solutions to nonlinear elliptic PDEs, which are the “observable” steady states of the corresponding evolutionary PDE. As we will see, these solutions turn out to have much nicer properties than general solutions, and in particular, we will study the following: are all stable solutions smooth, or may they have singularities?
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- Julio Daniel Rossi (Universidad de Buenos Aires, Argentina)
Convexity, partial differential equations and game theory
This course aims to explain in a self-contained way the main ideas behind the relation between convexity and partial differential equations (PDE).
We will develop the following material:
1. Introduction to fully nonlinear elliptic and parabolic PDE. Viscosity solutions, comparison arguments.
2. Classical convexity. Convex sets. Convex functions. Regularity results. Lipschitz continuity. Second-order differentiability, Aleksandroff theorem. Different notions of convexity.
3. The convex envelope of a boundary datum inside a domain. Characterization as a solution to the Dirichlet problem for a PDE. C^1-regularity.
4. A brief introduction to game theory and PDEs. A game for the convex envelope of a boundary datum.
Venue
The school will take place on 13th of July 2025 – 18th of July 2025 in Warsaw, at the Faculty of Mathematics, Informatics and Mechanics, University of Warsaw, Banacha 2, room 2180.