Abstract
We study the Γ-convergence of functionals arising in the Van der Waals–Cahn–Hilliard theory of phase transitions. Their limit is given as the sum of the area and the Willmore functional. The problem under investigation was proposed as modification of a conjecture of De Giorgi and partial results were obtained by several authors. We prove here the modified conjecture in space dimensions n = 2,3.
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This work was supported by the European Community’s Human Potential Programme under contract HPRN-CT-2002-00274, FRONTS-SINGULARITIES.
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Röger, M., Schätzle, R. On a Modified Conjecture of De Giorgi. Math. Z. 254, 675–714 (2006). https://doi.org/10.1007/s00209-006-0002-6
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DOI: https://doi.org/10.1007/s00209-006-0002-6