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International conference on Function Spaces and Approximation Theory dedicated to the 110th anniversary of S. M. Nikol'skii
May 25, 2015 12:50–13:30, Пленарные доклады, Moscow, Steklov Mathematical Institute of RAS
 


Sobolev Spaces, geometric function theory and its application

S. K. Vodop'yanov

Sobolev Institute of Mathematics, Siberian Branch of the Russian Academy of Sciences
Video records:
MP4 1,311.6 Mb
MP4 332.9 Mb
Materials:
Adobe PDF 492.1 Kb
Adobe PDF 230.4 Kb

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S. K. Vodop'yanov
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Abstract: We present new results obtained at the intersection of the theory of Sobolev spaces and geometric function theory. As an application we show a new approach to the definition of allowable deformations in variational problems of the nonlinear theory of elasticity, and a new method of proving the existence of extreme solutions.

Materials: Презентация_доклада.pdf (492.1 Kb), abstract.pdf (230.4 Kb)

References
  1. S. K. Vodopyanov, “O regulyarnosti otobrazhenii, obratnykh k sobolevskim”, Matem. sb., 203:10 (2012), 3–32  mathnet  crossref  mathscinet  zmath
  2. S. K. Vodopyanov, A. D. Ukhlov, “Operatory superpozitsii v prostranstvakh Soboleva”, Izvestiya VUZov. Matematika, 486:10 (2002), 11–33  mathnet  mathscinet
  3. Yu. G. Reshetnyak, Prostranstvennye otobrazheniya s ogranichennym iskazheniem, Nauka, Novosibirsk, 1982
  4. S. K. Vodopyanov, “O regulyarnosti funktsii Poletskogo pri slabykh analiticheskikh predpolozheniyakh iskhodnogo otobrazheniya”, Dokl. RAN, 455:2 (2014), 130–134  crossref  mathscinet  zmath
  5. A. N. Baikin, S. K. Vodopyanov, “Emkostnye otsenki, teoremy tipa Liuvillya i ob ustranenii osobennostei dlya otobrazhenii s ogranichennym $(p,q)$-iskazheniem”, Sib. mat. zhurn., 56:2 (2015), 290–321  mathnet
  6. J. M. Ball, “Convexity conditions and existence theorems in nonlinear elasticity”, Arch. Ration. Mech. and Analys, 63 (1977), 337–403  crossref  mathscinet  zmath  scopus
  7. S. K. Vodopyanov, A. O. Molchanova, “Variatsionnye zadachi nelineinoi teorii uprugosti v nekotorykh klassakh otobrazhenii s konechnym iskazheniem”, Dokl. RAN, 2015 (в печати)


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