Droplet Minimizers of an Isoperimetric Problem with Long‐Range Interactions
By Marco Cicalese, Emanuele Spadaro. 2011
84 citations recorded by the source corpus.
We give a detailed description of the geometry of single‐droplet patterns in a nonlocal isoperimetric problem. In particular, we focus on the sharp interface limit of the Ohta‐Kawasaki free energy for diblock copolymers, regarded as a paradigm for energies with short‐ and long‐range interactions. Exploiting fine properties of the regularity theory for minimal surfaces, we extend previous partial results in different directions and give robust tools for the geometric analysis of more complex patterns. © 2012 Wiley Periodicals inc.
Subfields: Computational Theory and Mathematics, Fluid Flow and Transfer Processes, Materials Chemistry
View Paper: https://www.semanticscholar.org/paper/713b8f98b8be438315685be11bccf26351d3863b
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In Computational Theory and Mathematics
In Fluid Flow and Transfer Processes
In Materials Chemistry
Citations in the corpus
- Sharp gradient stability for the Sobolev inequality (2020, background): “Introduction Motivated by important applications to problems in the calculus of variations and evolution PDEs, in recent years there has been a growing interest around the understanding of quantitative stability for functional/geometric inequalities, see for instance [3, 2, 8, 27, 28, 21, 9, 22, 29,”
- On an Isoperimetric Problem with a Competing Nonlocal Term II: The General Case (2012, result): “Let us mention that some related recent results for the ndimensional Coulombic case on bounded domains were obtained in [10].”