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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


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
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.