TY - JOUR
T1 - A weighted gradient theory of phase transitions with a possibly singular and degenerate spatial inhomogeneity
AU - Palatucci, Giampiero
AU - Valdinoci, Enrico
PY - 2012/3/1
Y1 - 2012/3/1
N2 - This paper studies the asymptotic behavior of a perturbed variational problem for the Cahn-Hilliard theory of phase transitions in a fluid, with spatial inhomogeneities in the internal free energy term. The inhomogeneous term can vanish or become infinite and it can also behave as an appropriate power of the distance from the boundary.The standard minimal interface criterion will be recovered even in spite of such severe degeneracies and/or singularities.
AB - This paper studies the asymptotic behavior of a perturbed variational problem for the Cahn-Hilliard theory of phase transitions in a fluid, with spatial inhomogeneities in the internal free energy term. The inhomogeneous term can vanish or become infinite and it can also behave as an appropriate power of the distance from the boundary.The standard minimal interface criterion will be recovered even in spite of such severe degeneracies and/or singularities.
KW - Γ-convergence
KW - Functions of bounded variation
KW - Phase transitions
KW - Singular perturbation
KW - Spatial inhomogeneity
UR - http://www.scopus.com/inward/record.url?scp=84855597479&partnerID=8YFLogxK
U2 - 10.1016/j.jde.2011.12.005
DO - 10.1016/j.jde.2011.12.005
M3 - Article
AN - SCOPUS:84855597479
SN - 0022-0396
VL - 252
SP - 3381
EP - 3402
JO - Journal of Differential Equations
JF - Journal of Differential Equations
IS - 5
ER -