3 papers
math.FA2025
Smoothness of weight sharply discards Lavrentiev's gap for double phase functionals
MichaÅ Borowski
We show that the smoother the weight, the broader the range of exponents for which the Lavrentiev's gap is absent for the double phase functionals, i.e., $u \mapsto \int_Ω \left(|…
math.AP2025
Discarding Lavrentiev's Gap in Non-autonomous and Non-Convex Variational Problems
MichaÅ 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_Î…
math.OC2025
Convergence of projected stochastic approximation algorithm
MichaÅ Borowski, BÅażej Miasojedow
We study the Robbins-Monro stochastic approximation algorithm with projections on a hyperrectangle and prove its convergence. This work fills a gap in the convergence proof of the…