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Explore modern trends in Gagliardo-Nirenberg inequality through this 26-minute conference talk delivered by Tomáš Roskovec at the Erwin Schrödinger International Institute for Mathematics and Physics (ESI). Delve into the evolution of this fundamental inequality since its original formulation in 1959, examining various generalizations and refinements. Learn about the choice of spaces generating functionals A, B, and C, methods for verifying optimality, cases involving fractional derivatives, and potential nonlinearities on the right-hand side. Gain insights from both established and unpublished research in this field, presented as part of the Workshop on "Between Regularity and Defects: Variational and Geometrical Methods in Materials Science" held at ESI in February 2023.
