2026 Analysis on Metric Space Seminar: "The Trace Theorem for Sobolev Homeomorphisms" by Dr.Aleksis Koski, Aalto University

Speaker: Aleksis Koski, Aalto University

Title:The Trace Theorem for Sobolev Homeomorphisms

Abstract: Classical Sobolev trace theory tells us when a boundary map can be extended as a Sobolev function inside a given domain in R^n. For the purposes of minimization problems in Nonlinear Elasticity, it is natural to rephrase this question in the context of extending a given embedding of the boundary as a homeomorphic Sobolev map. In this talk, I will explain what is known about this problem, ending with a full trace theory for Sobolev homeomorphisms in 2D.

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