The geometric structure of interfaces and free boundaries

DOI10.4171/MAG-17zbMath1504.76094MaRDI QIDQ2076016

Joaquim Serra

Publication date: 17 February 2022

Published in: European Mathematical Society Magazine (Search for Journal in Brave)

zbMATH Keywords

regularityminimal surfacephase transitionStefan problemnonlinear elliptic equationobstacle problemAllen-Cahn equationbinary fluidPeierls-Nabarro equation

Mathematics Subject Classification ID

Variational inequalities (49J40) PDEs in connection with fluid mechanics (35Q35) Multiphase and multicomponent flows (76T99) Minimal surfaces and optimization (49Q05)

Cites Work

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• On the oriented Plateau problem
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• On the singular set of the parabolic obstacle problem
• An example of generic regularity for a non-linear elliptic equation
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• The obstacle problem revisited
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• On the number of singularities for the obstacle problem in two dimensions
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• Global minimizers of the Allen-Cahn equation in dimension \(n\geq 8\)
• On the fine structure of the free boundary for the classical obstacle problem
• A homogeneity improvement approach to the obstacle problem
• On stable solutions for boundary reactions: a De Giorgi-type result in dimension \(4 + 1\)
• Quantitative flatness results and \(BV\)-estimates for stable nonlocal minimal surfaces
• A logarithmic epiperimetric inequality for the obstacle problem
• Second order estimate on transition layers
• Regularity of flat level sets in phase transitions
• Boundary vortices in thin magnetic films
• Some interior regularity theorems for minimal surfaces and an extension of Bernstein's theorem
• Minimal varieties in Riemannian manifolds
• Minimal cones and the Bernstein problem
• Entire solutions of semilinear elliptic equations in ℝ³ and a conjecture of De Giorgi
• Uniform convergence of a singular perturbation problem
• The singular sets of area minimizing rectifiable currents with codimension one and of area minimizing flat chains modulo two with arbitrary codimension

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