caa a22 4500 605515247 CHVBK 20210128100708.0 cr unu---uuuuu 210128e20150101xx s 000 0 eng 10.1007/s00205-014-0777-2 doi (NATIONALLICENCE)springer-10.1007/s00205-014-0777-2 Quasistatic Droplets in Randomly Perforated Domains [Elektronische Daten] [Nestor Guillen, Inwon Kim] We consider the Hele-Shaw problem in a randomly perforated domain with zero Neumann boundary conditions. A homogenization limit is obtained as the characteristic scale of the domain goes to zero. Specifically, we prove that the solutions as well as their free boundaries converge uniformly to those corresponding to a homogeneous and anisotropic Hele-Shaw problem set in $${\mathbb{R}^{d}}$$ R d . The main challenge when deriving the limit lies in controlling the oscillations of the free boundary. This is overcome first by extending De Giorgi-Nash-Moser type estimates to perforated domains and second by proving the almost sure non-degenerate growth of the solution near its free boundary. Springer-Verlag Berlin Heidelberg, 2014 Guillen Nestor Department of Mathematics, UCLA, Los Angeles, USA aut Kim Inwon Department of Mathematics, UCLA, Los Angeles, USA aut Archive for Rational Mechanics and Analysis Springer Berlin Heidelberg 215/1(2015-01-01), 211-281 0003-9527 215:1<211 2015 215 205 https://doi.org/10.1007/s00205-014-0777-2 text/html Onlinezugriff via DOI BK010053 XK010053 XK010000 Metadata rights reserved Springer special CC-BY-NC licence nationallicence 1 research-article jats NATIONALLICENCE NATIONALLICENCE NL-springer NATIONALLICENCE 856 40 https://doi.org/10.1007/s00205-014-0777-2 text/html Onlinezugriff via DOI NATIONALLICENCE 700 1- Guillen Nestor Department of Mathematics, UCLA, Los Angeles, USA aut NATIONALLICENCE 700 1- Kim Inwon Department of Mathematics, UCLA, Los Angeles, USA aut NATIONALLICENCE 773 0- Archive for Rational Mechanics and Analysis Springer Berlin Heidelberg 215/1(2015-01-01), 211-281 0003-9527 215:1<211 2015 215 205