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Nonlinear Analysis

Endpoint estimates in Lorentz spaces for vector fields

Jean Van Schaftingen, Universite Catholique de Louvain, Belgium

Location:  Hill 705
Date & time: Tuesday, 30 October 2018 at 1:40PM - 3:00PM

Abstract: Endpoint Gagliardo-Nirenberg-Sobolev embeddings have been known to hold for vector fields with an estimate that depends on a smaller set of combinations of the full derivative of the vector field, such as the differential and codifferential (J. Bourgain and H. Brezis, 2004) or the symmetric part of the derivative (M.J. Strauss, 1973).   On the other hand, A. Alvino has obtained in 1977 the corresponding scalar endpoint estimate in the scale of Lorentz spaces. I will present a new family of endpoint Lorentz estimates for vector fields.

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