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math.AP2021
Existence of minimisers of variational problems posed in spaces of mixed smoothness
Adam Prosinski
The present work constitutes a first step towards establishing a systematic framework for treating variational problems that depend on a given input function through a mixture of i…
math.AP2017
Closed - Quasiconvexity and Variational Problems with Extended Real-Valued Integrands
Adam Prosinski
This paper relates the lower semi-continuity of an integral functional in the compensated compactness setting of vector fields satisfying a constant-rank first-order differential c…
math.AP2016
Global-in-time regularity via duality for congestion-penalized Mean Field Games
Adam Prosinski, Filippo Santambrogio
After a brief introduction to one of the most typical problems in Mean Field Games, the congestion case (where agents pay a cost depending on the density of the regions they visit)…