The course is subdivided in three parts, which may vary in size and content according to the interests of the audience. 1. Nonlocal discrete systems. We consider simple boundary value problems on sets of integers depending on a function minimizing a nonconvex interaction potential and a longrange convex energy. Our goal is to describe the interaction between nonconvexity and nonlocality through asymptotic properties of solutions and of minima as the size of the domain of minimization diverges. Some lessons will be devoted to analogous problems from the standpoint of dynamical systems;2. Convergence of gradient flows for freediscontinuity problems.We consider minimizingmovements in one dimension for the MumfordShah functional and some of its approximations, showing convergence and nonconvergence results;3. Relaxation of nonlocal energies.We analyze the lower semicontinuous envelope of nonconvex energies depending on a double integrals, which leads to nonintegral functionals.
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Topics in the Calculus of Variations
Lecturer:
Course Type:
PhD Course
Academic Year:
20212022
Period:
NovemberSeptember
Duration:
60 h
Description:
Research Group:
Location:
A133
Location:
April 5 room 134, April 7 room 131, April 8 room 133
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Cristiana De Filippis
Nonlinear potentials at the fractional scale: sharp regularity
Thursday, November 30, 2023  14:00

Pablo Alexei Gazca Orozco
Numerical computations and thermodynamically complete models for inelastic behaviour in solids
Monday, December 4, 2023  15:00

Paolo Piersanti
Variational Inequalities and their applications in elasticity and glaciology
Wednesday, December 6, 2023  15:00

Daniele Semola
Ricci Curvature, Fundamental Groups, and the Milnor Conjecture
Thursday, December 7, 2023  14:00 to 15:30
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