117 citations · 335 across the 29 of their papers we have counts for
35 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)\…
Langevin Monte Carlo Beyond Lipschitz Gradient Continuity
Matej Benko, Iwona Chlebicka, Jørgen Endal +1
We present a significant advancement in the field of Langevin Monte Carlo (LMC) methods by introducing the Inexact Proximal Langevin Algorithm (IPLA). This novel algorithm broadens…
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…
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 \[\partial_tμ=\rm{div}(μ\nabla V)+\rm{div}(μ(\nabla W \ast μ))+Δμ\,,\] within a large and natural class of the confineme…
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 , . The…
Riesz potential estimates for mixed local-nonlocal problems with measure data
Iwona Chlebicka, Kyeong Song, Yeonghun Youn +1
We study gradient regularity for mixed local-nonlocal problems modelled upon \[ -Δ_p u +(-Δ_p)^su=μ\qquad\text{for} \quad 2-\tfrac{1}{n}<p<\infty\quad \text{and}\quad s\in(0,1)\,,\…
Gradient Riesz potential estimates for a general class of measure data quasilinear systems
Iwona Chlebicka, Minhyun Kim, Marvin Weidner
We study the gradient regularity of solutions to measure data elliptic systems with Uhlenbeck-type structure and Orlicz growth. For any bounded Borel measure, pointwise estimates f…
Solidarity of Gibbs Samplers: the spectral gap
Iwona Chlebicka, Krzysztof Łatuszyński, Błażej Miasojedow
Gibbs samplers are preeminent Markov chain Monte Carlo algorithms used in computational physics and statistical computing. Yet, their most fundamental properties, such as relations…
A direct proof of existence of weak solutions to fully anisotropic and inhomogeneous elliptic problems
Iwona Chlebicka, Arttu Karppinen, Ying Li
We provide a direct proof of existence and uniqueness of weak solutions to a broad family of strongly nonlinear elliptic equations with lower order terms. The leading part of the o…
Absence and presence of Lavrentiev's phenomenon for double phase functionals upon every choice of exponents
Michał Borowski, Iwona Chlebicka, Filomena De Filippis +1
We study classes of weights ensuring the absence and presence of the Lavrentiev's phenomenon for double phase functionals upon every choice of exponents. We introduce a new sharp s…
Absence of Lavrentiev's gap for anisotropic functionals
Michał Borowski, Iwona Chlebicka, Błażej Miasojedow
We establish the absence of the Lavrentiev gap between Sobolev and smooth maps for a non-autonomous variational problem of a general structure, where the integrand is assumed to be…
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…
Controlling monotonicity of nonlinear operators
Michał Borowski, Iwona Chlebicka
Controlling the monotonicity and growth of Leray--Lions' operators including the -Laplacian plays a fundamental role in the theory of existence and regularity of solutions to se…
Functional inequalities and applications to doubly nonlinear diffusion equations
Iwona Chlebicka, Nikita Simonov
We study weighted inequalities of Hardy and Hardy-Poincaré type and find necessary and sufficient conditions on the weights so that the considered inequalities hold. Examples with…
Measure data systems with Orlicz growth
Iwona Chlebicka, Yeonghun Youn, Anna Zatorska-Goldstein
We study the existence of very weak solutions to a system \[\begin{cases}-\mathrm{div} \mathcal{A}(x,D\mathbf{u})=\mathbfμ\quad\text{in }\ Ω, \mathbf{u}=0\quad\text{on }\ \partialΩ…
Wolff potentials and measure data vectorial problems with Orlicz growth
Iwona Chlebicka, Yeonghun Youn, Anna Zatorska-Goldstein
We study solutions to measure data elliptic systems with Uhlenbeck-type structure that involve operator of divergence form, depending continuously on the spacial variable, and expo…
Measure data elliptic problems with generalized Orlicz growth
Iwona Chlebicka
We study nonlinear measure data elliptic problems involving the operator exposing generalized Orlicz growth. Our framework embraces reflexive Orlicz spaces, as well as natural vari…
Essentially fully anisotropic Orlicz functions and uniqueness to measure data problem
Iwona Chlebicka, Piotr Nayar
Studying elliptic measure data problem with strongly nonlinear operator whose growth is described by the means of fully anisotropic -function, we prove the uniqueness for a broa…
Wolff potentials and local behaviour of solutions to measure data elliptic problems with Orlicz growth
Iwona Chlebicka, Flavia Giannetti, Anna Zatorska-Goldstein
We establish pointwise estimates expressed in terms of a nonlinear potential of a generalized Wolff type for -superharmonic functions with nonlinear operator $A:Ω\times\mathbb{R…
Generalized superharmonic functions with strongly nonlinear operator
Iwona Chlebicka, Anna Zatorska-Goldstein
We study properties of -harmonic and -superharmonic functions involving an operator having generalized Orlicz-growth embracing besides Orlicz case also na…
Boundary regularity for manifold constrained -harmonic maps
Iwona Chlebicka, Cristiana De Filippis, Lukas Koch
We prove partial and full boundary regularity for manifold constrained -harmonic maps.
Removable sets in elliptic equations with Musielak-Orlicz growth
Iwona Chlebicka, Arttu Karppinen
We characterize, in the terms of intrinsic Hausdorff measures, the size of~removable sets for Hölder continuous solutions to elliptic equations with Musielak-Orlicz growth. In the…