# Higher-order phase transitions with line-tension effect

ESAIM: Control, Optimisation and Calculus of Variations (2011)

- Volume: 17, Issue: 3, page 603-647
- ISSN: 1292-8119

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topGalvão-Sousa, Bernardo. "Higher-order phase transitions with line-tension effect." ESAIM: Control, Optimisation and Calculus of Variations 17.3 (2011): 603-647. <http://eudml.org/doc/272912>.

@article{Galvão2011,

abstract = {The behavior of energy minimizers at the boundary of the domain is of great importance in the Van de Waals-Cahn-Hilliard theory for fluid-fluid phase transitions, since it describes the effect of the container walls on the configuration of the liquid. This problem, also known as the liquid-drop problem, was studied by Modica in [Ann. Inst. Henri Poincaré, Anal. non linéaire 4 (1987) 487–512], and in a different form by Alberti et al. in [Arch. Rational Mech. Anal.u is a scalar density function and W and Vare double-well potentials, the exact scaling law is identified in the critical regime, when $\varepsilon \lambda _\{\varepsilon \}^\{\frac\{2\}\{3\}\} \sim 1$.},

author = {Galvão-Sousa, Bernardo},

journal = {ESAIM: Control, Optimisation and Calculus of Variations},

keywords = {gamma limit; functions of bounded variations; functions of bounded variations on manifolds; phase transitions; limit},

language = {eng},

number = {3},

pages = {603-647},

publisher = {EDP-Sciences},

title = {Higher-order phase transitions with line-tension effect},

url = {http://eudml.org/doc/272912},

volume = {17},

year = {2011},

}

TY - JOUR

AU - Galvão-Sousa, Bernardo

TI - Higher-order phase transitions with line-tension effect

JO - ESAIM: Control, Optimisation and Calculus of Variations

PY - 2011

PB - EDP-Sciences

VL - 17

IS - 3

SP - 603

EP - 647

AB - The behavior of energy minimizers at the boundary of the domain is of great importance in the Van de Waals-Cahn-Hilliard theory for fluid-fluid phase transitions, since it describes the effect of the container walls on the configuration of the liquid. This problem, also known as the liquid-drop problem, was studied by Modica in [Ann. Inst. Henri Poincaré, Anal. non linéaire 4 (1987) 487–512], and in a different form by Alberti et al. in [Arch. Rational Mech. Anal.u is a scalar density function and W and Vare double-well potentials, the exact scaling law is identified in the critical regime, when $\varepsilon \lambda _{\varepsilon }^{\frac{2}{3}} \sim 1$.

LA - eng

KW - gamma limit; functions of bounded variations; functions of bounded variations on manifolds; phase transitions; limit

UR - http://eudml.org/doc/272912

ER -

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