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Mat. Sb., 1996, Volume 187, Number 1, Pages 3–16 (Mi msb97)  

This article is cited in 6 scientific papers (total in 6 papers)

Existence theorems for boundary-value problems of hyperelasticity

I. A. Brigadnov

North-Western Correspondence Technical Institute

Abstract: The variational formulation of the boundary-value problem of elastostatics for hyperelastic materials are considered. The existence of a solution on the space $W^{1,p}(\Omega,\mathbb R^3)$, $p>1$, is proved for standard outside influences under the most general assumptions on the potential with superlinear growth in the modulus of the matrix argument. Counterexamples are given showing that the condition of coercivity is best possible. In the proof of the existence theorem the weak convergence of the determinants of the gradients of the maps for the minimizing sequence is not used. This enable us to generalize significantly Ball's results. The condition of preservation of orientation (or of incompressibility) almost everywhere in the domain for a global minimizer is proved directly.

DOI: https://doi.org/10.4213/sm97

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English version:
Sbornik: Mathematics, 1996, 187:1, 1–14

Bibliographic databases:

UDC: 517.97+539.3
MSC: Primary 35A15; Secondary 35Q72
Received: 19.01.1995

Citation: I. A. Brigadnov, “Existence theorems for boundary-value problems of hyperelasticity”, Mat. Sb., 187:1 (1996), 3–16; Sb. Math., 187:1 (1996), 1–14

Citation in format AMSBIB
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    Erratum

    This publication is cited in the following articles:
    1. Brigadnov, IA, “Existence theorems for boundary-value problems of hyperelasticity (vol 187, pg 3, 1996)”, Sbornik Mathematics, 188:11–12 (1997), 1729  crossref  mathscinet  isi
    2. Brigadnov I.A., “The limited static load in finite elasticity”, Constitutive Models For Rubber, 1999, 37–43  isi
    3. A. A. Makhnev, “Partial geometries, their extensions, and related graphs”, Journal of Mathematical Sciences (New York), 102:3 (2000), 4009  crossref  mathscinet  zmath  scopus  scopus  scopus
    4. Brigadnov, IA, “Duality method for limit analysis of dielectrics in powerful electric fields”, Journal of Computational and Applied Mathematics, 168:1–2 (2004), 87  crossref  mathscinet  zmath  adsnasa  isi  elib  scopus  scopus  scopus
    5. Brigadnov I.A., “Limit analysis method in electrostatics”, Numerical Mathematics and Advanced Applications, Proceedings, 2004, 176–185  crossref  mathscinet  zmath  isi
    6. Igor A. Brigadnov, “Limit analysis method in elastostatics and electrostatics”, Math Meth Appl Sci, 28:3 (2005), 253  crossref  mathscinet  zmath  isi  elib  scopus  scopus  scopus
  • Математический сборник - 1992–2005 Sbornik: Mathematics (from 1967)
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