Steklov Mathematical Institute, Russian Academy of Sciences
E-mail: ,
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Keywords: Sobolev spaces, Besov spaces, metric spaces with measure, geometrical analysis.
Education:
→ 2009 – Bachelor degree, MIPT;
→ 2011 – Master degree, MIPT;
→ 2014 – Ph.D. Thesis (Steklov Institute).
Teaching: since 2011 works at the Department of Higher Mathematics, MIPT, Assosiate Professor.
Publications (recent):
2023
→ A. I. Tyulenev, "Traces of Sobolev Spaces on Piecewise Ahlfors–David Regular Sets", Math. Notes, 114:3 (2023), 351–376, DOI.
→ A. I. Tyulenev, "Traces of Sobolev spaces to irregular subsets of metric measure spaces", Mat. Sb., 214:9 (2023), 58–143, DOI.
2022
→ A.I. Tyulenev, "Restrictions of Sobolev \(W^1_p(\mathbb{R}^2)\)-spaces to planar rectifiable curves", Ann. Fenn. Math., 47:1 (2022), 507–531, arXiv.
→ A.I. Tyulenev, "Nekotorye svoistva mnozhestv tipa poristosti, svyazannye s \(d\)-obkhvatom po Khausdorfu", Teoriya priblizhenii, funktsionalnyi analiz i prilozheniya, Sbornik statei. K 70-letiyu akademika Borisa Sergeevicha Kashina, Trudy MIAN, 319, MIAN, M., 2022, 298–323, arXiv, DOI.
2021
→ N. Gigli, A. Tyulenev, "Korevaar–Schoen's directional energy and Ambrosio's regular Lagrangian flows", Math. Z., 298 (2021), 1221–1261, arXiv, DOI.
→ A.I. Tyulenev, "Almost sharp descriptions of traces of Sobolev \(W^1_p(\mathbb{R}^n)\)-spaces to arbitrary compact subsets of \(\mathbb{R}^n\). The case \(p \in (1,n]\)", 2021, 60 pp., arXiv.
→ N. Gigli, A. Tyulenev, "Korevaar–Schoen's energy on strongly rectifiable spaces", Calc. Var. Partial Differential Equations, 60 (2021), 235, 54 pp., arXiv, DOI.
→ A. I. Tyulenev, "Almost Sharp Descriptions of Traces of Sobolev Spaces on Compacta", Math. Notes, 110:6 (2021), 976–980, DOI.
→ "Funktsionalnye prostranstva, teoriya priblizhenii i smezhnye voprosy analiza, Sbornik statei. K 115-letiyu so dnya rozhdeniya akademika Sergeya Mikhailovicha Nikolskogo", Trudy MIAN, 312, ed. O. V. Besov, A. I. Tyulenev, MIAN, M., 2021 , 338 pp.
2020
→ S.K. Vodopyanov, A.I. Tyulenev, "Sobolev \(W^1_p\)-spaces on \(d\)-thick closed subsets of \(\mathbb R^n\)", Sb. Math., 211:6 (2020), 786–837, DOI.