1 citations · 2 across the 4 of their papers we have counts for
4 papers
Smoothness of weight sharply discards Lavrentiev's gap for double phase functionals
Michał 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(|\…
Convergence of projected stochastic approximation algorithm
Michał Borowski, Błażej 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…
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…
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…