Titulo: The Caffarelli-Kohn-Nirenberg inequality: a parametric analysis.
Palestrante: Aldo Bazán (UFF)
Data: 29 de agosto de 2019 (quinta-feira)
Horário: Instituto de Matemática – Bloco C – Sala C119 – Ilha do Fundão
Resumo: Functional inequalities involving integrals appear quite frequently in estimates and problems of regularity of solutions of partial differential equations, as a consequence of the use of functional spaces that depend on the concept of integral. A simplified version of the inequality presented here appears for the first time in , in the analysis of a type of weak solutions of the Navier Stokes equation, and later in its general form in .
Since it appeared, various modifications and applications have emerged, such as in rigidity problems of differentiable manifolds and in measurement spaces where it is necessary to use alternative definitions to the usual idea of derivative. In this talk, we will give a new proof of the Caffarelli-Kohn-Nirenberg inequality, defining a new real parameter, which is a consequence of the relationships between the original parameters that appear in this inequality.
 L.A. Caffarelli, R. Kohn, L. Nirenberg,First order interpolation inequalities with weights, Compositio Math.53(1984), 259–275.
 L.A. Caffarelli, R. Kohn, L. Nirenberg,Partial regularity of suitable weak solutions of the Navier-Stokes equa-tions, Comm. Pure Appl. Math.35(1982), 771–831.