339 citations · 551 across the 39 of their papers we have counts for
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Lipschitz stability for Bayesian inference in porous medium tissue growth models
Tomasz Dębiec, Piotr Gwiazda, Błażej Miasojedow +3
We consider a macroscopic model for the dynamics of living tissues incorporating pressure-driven dispersal and pressure-modulated proliferation. Given a power-law constitutive rela…
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…
Stability of solutions of the porous medium equation with growth with respect to the diffusion exponent
Tomasz Dębiec, Piotr Gwiazda, Błażej Miasojedow +1
We consider a macroscopic model for the growth of living tissues incorporating pressure-driven dispersal and pressure-modulated proliferation. Assuming a power-law relation between…
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…