Jani Onninen

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math.CV2026

Values of finite distortion: Reshetnyak's theorem, the Liouville theorem, and the Lusin (N) -property

Ilmari Kangasniemi, Jani Onninen, Yizhe Zhu

Let $I^c ◯ \subset R^{n}$ be a domain and $f \in W_{loc}^{1, n} (I^c ◯, R^{n})$ . We say that $f$ has a value of finite distortion at $y_{0} \in R^{n}$ if there exi…

math.CV2025

Continuity for Sobolev mappings with null Lagrangian bounds

Ilmari Kangasniemi, Jani Onninen

We prove the continuity of Sobolev functions $I ¨ \in W_{loc}^{1, n} (I^c ◯)$ , $I^c ◯ \subset R^{n}$ , that satisfy \[ \lvert\nabla Ï(x)\rvert^n \le K(x)\bigl(\langle \nabla Ï…

math.CV2025

Characterizing Sobolev Homeomorphic Extensions via Internal Distances

Aleksis Koski, Jani Onninen, Haiqing Xu

We give a full characterization of embeddings of the unit circle that admit a Sobolev homeomorphic extension to the unit disk. As a direct corollary, we establish that for quasicon…

math.CV2024

Complex Harmonic Capacitors

Tadeusz Iwaniec, Jani Onninen, Teresa Radice

The concept of complex harmonic potential in a doubly connected condenser (capacitor) is introduced as an analogue of the real-valued potential of an electrostatic vector field. In…

math.CV2024

Linear distortion and rescaling for quasiregular values

Ilmari Kangasniemi, Jani Onninen

Sobolev mappings exhibiting only pointwise quasiregularity-type bounds have arisen in various applications, leading to a recently developed theory of quasiregular values. In this a…