7 papers
Born Discrete, Made Smooth: Variational Formulation of Shallow Neural Networks
Matej Benko, Pierre Bousquet, Iwona Chlebicka +1
Although neural networks are remarkably effective, their underlying optimization principles remain theoretically elusive, often characterized by non-convex landscapes and stochasti…
Orlicz Potential Theory: Balayage, Riesz Measures, and Very Weak Solutions
Iwona Chlebicka, Minhyun Kim, Ying Li +1
We develop a nonlinear potential theory for elliptic equations with Orlicz growth under general monotonicity and growth conditions, without any homogeneity or scaling assumptions.…
Gradient higher integrability of bounded solutions to parabolic double-phase systems
Iwona Chlebicka, Prashanta Garain, Wontae Kim
We prove that bounded solutions to degenerate parabolic double-phase problem modelled upon \[u_t-\dv(|\na u|^{p-2}\na u+a(x,t)|\na u|^{q-2}\na u)=-\dv(|F|^{p-2}F+a(x,t)|F|^{q-2}F)\…
Convergence rates of particle approximation of forward-backward splitting algorithm for granular medium equations
Matej Benko, Iwona Chlebicka, Jørgen Endal +1
We study the spatially homogeneous granular medium equation \[\partial_tμ=\rm{div}(μ\nabla V)+\rm{div}(μ(\nabla W \ast μ))+Îμ\,,\] within a large and natural class of the con…
Refined asymptotics for the Cauchy problem for the fast -Laplace evolution equation
Matteo Bonforte, Iwona Chlebicka, Nikita Simonov
Our focus is on the fast diffusion equation driven by the -Laplacian operator, that is with , posed in the whole space , . Th…
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…