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Time Evolution of Elastically Starlike Domains in the Hele‐Shaw Flow Problem

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  • Mihai Aron

Abstract

The notion of elasticity and the associated concept of elastically starlike functions are newly introduced in geometric function theory and are developed in this paper. The terminology is motivated by the geometric interpretation of elasticity as a measure of the deformation of level lines under conformal mappings. We investigate the connection between elastically starlike and starlike functions, and we apply these ideas to the Hele‐Shaw flow problem with zero surface tension. We show that if the initial fluid domain is starlike and the boundary elasticity is bounded above and below by positive constants depending on the geometry of the initial domain, then this geometric structure is preserved throughout the existence time of the solution.

Suggested Citation

  • Mihai Aron, 2026. "Time Evolution of Elastically Starlike Domains in the Hele‐Shaw Flow Problem," Mathematische Nachrichten, Wiley Blackwell, vol. 299(9), pages 2452-2471, September.
    • Handle: RePEc:bla:mathna:v:299:y:2026:i:9:p:2452-2471
    DOI: 10.1002/mana.70200
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