Melanie Rupflin, "Quantitative analysis of variational problems and PDEs"
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Europe/Rome
Ex-ISEF/Building-Main Lecture Hall (GSSI)
Ex-ISEF/Building-Main Lecture Hall
GSSI
20
Description
Abstract: A fundamental question in the analysis of variational problems is whether functions that almost minimise a given energy, or almost solve the Euler-Lagrange equation, provide good approximations of true minimisers or exact solutions of PDEs.
In practice one wants to understand this question not only at a qualitative level, but to establish rigorous quantitative results that provide bounds on the distance between approximate solutions and exact solutions in terms of (suitable powers) of the norm of the error in the PDE respectively the energy defect.
In this talk we will see that natural phenomena, such as the concentration of energy at different scales, cause a break-down of the classical theory even for simple model energies such as the Dirichlet energy for maps into the unit sphere, and report on some recent progress in the quantitative analysis of such variational problems.
