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math.AP2025
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…
math.AP2025
Lipschitz stability for Bayesian inference in porous medium tissue growth models
Tomasz DÄbiec, Piotr Gwiazda, BÅażej 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…
math.AP2024
Stability of solutions of the porous medium equation with growth with respect to the diffusion exponent
Tomasz DÄbiec, Piotr Gwiazda, BÅażej 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…