|
Chiffres-clé
Chiffres clefs
189 personnes travaillent au LJLL
86 permanents
80 chercheurs et enseignants-chercheurs permanents
6 ingénieurs, techniciens et personnels administratifs
103 personnels non permanents
74 doctorants
15 post-doc et ATER
14 émérites et collaborateurs bénévoles
Chiffres janvier 2022
A voir
Séminaire du LJLL - 01 10 2021 14h00 : G. Mingione
Vendredi 01 octobre 2021 — 14h00
Exposé à distance avec retransmission par Zoom
Giuseppe Mingione (Université de Parme)
Nonlinear versions of linear theories : from linear to nonlinear gradient estimates for elliptic equations
Résumé
Linear theories as Calderón and Zygmund theory of singular integrals and classical potential estimates are basic issues where Harmonic Analysis tools come to the rescue in Partial Differential Equations estimates. Sharp regularity results and fine properties of solutions can be obtained through the use of singular and fractional integrals via pointwise estimates implied by the existence of fundamental solutions. While such approaches are obviously linear, in the last years there has been a number of results outlining a complete parallel in the nonlinear case, i.e. where nonlinear equations are considered. In this case, nonlinear potentials replace linear ones as pioneered by Maz’ya and Havin. In fact, pointwise bounds can be found for solutions, finally reaching a unified approach between linear and nonlinear problems. I will try to outline recent developments in such directions.