5 papers · 1 filter
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)\…
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…
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 }\ \partia…