Moving interfaces–and in the stationary case, free boundaries–are ubiquitous in our
environment and daily life. They are at the basis of many physical, chemical, and also …

..." What do you call work?"" Why ain't that work?" Tom resumed his whitewashing, and
answered carelessly:" Well. lI1a), he it is, and maybe it aill't. All I know, is, it suits Tom …

Convergent numerical schemes for degenerate elliptic partial differential equations are
constructed and implemented. Simple conditions are identified which ensure that nonlinear …

The classical Stefan model is a free boundary problem that represents thermal processes in
phase transitions just by accounting for heat-diffusion and exchange of latent heat. The …

We provide existence of a unique smooth solution for a class of one-and two-phase Stefan
problems with Gibbs-Thomson correction in arbitrary space dimensions. In addition, it is …

In this paper we introduce a notion of viscosity solutions for the one-phase Hele-Shaw and
Stefan problems when there is no surface tension. We prove the uniqueness and existence …

Mathematische Annalen Page 1 Math. Ann. (2007) 338:703–755 DOI 10.1007/s00208-007-0094-2
Mathematische Annalen Existence of analytic solutions for the classical Stefan problem Jan …

The free boundary problem for a two‐dimensional fluid permeating a porous medium is
studied. This is known as the one‐phase Muskat problem and is mathematically equivalent …

In this paper we consider entire solutions to semilinear elliptic equations. We show that
solutions that are monotone in one direction are energy minimizers and we discuss …

(P) Au—ut= 0 in£>\9 {u> 0}, u= 0,(u+) 2—(u~) 2= 2M on T> C\d {u> 0}, in a viscosity sense,
and in a pointwise sense at regular free boundar Here v is the inward unit spacial normal to …