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math.AP2024★ 1 cited
Discarding Lavrentiev's Gap in Non-autonomous and Non-Convex Variational Problems
Michał Borowski, Pierre Bousquet, Iwona Chlebicka +2
We establish that the Lavrentiev gap between Sobolev and Lipschitz maps does not occur for a scalar variational problem of the form: \[ \textrm{to minimize} \qquad u \mapsto \int_Ω…
math.AP2022★ 1 cited
Boundedness of Wolff-type potentials and applications to PDEs
Michał Borowski, Iwona Chlebicka, Błażej Miasojedow
We provide a short proof of a sharp rearrangement estimate for a generalized version of a potential of Wolff--Havin--Maz'ya type. As a consequence, we prove a reduction principle f…