On Neumann's problem for a quasilinear differential system of the finite elastostatics type. Local theorems of existence and uniqueness

M. Lanza De Cristoforis; T. Valent

Rendiconti del Seminario Matematico della Università di Padova (1982)

  • Volume: 68, page 183-206
  • ISSN: 0041-8994

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Lanza De Cristoforis, M., and Valent, T.. "On Neumann's problem for a quasilinear differential system of the finite elastostatics type. Local theorems of existence and uniqueness." Rendiconti del Seminario Matematico della Università di Padova 68 (1982): 183-206. <http://eudml.org/doc/107871>.

@article{LanzaDeCristoforis1982,
author = {Lanza De Cristoforis, M., Valent, T.},
journal = {Rendiconti del Seminario Matematico della Università di Padova},
keywords = {Neumann's problem; quasilinear differential system; elastostatics; existence; uniqueness; dead traction problem},
language = {eng},
pages = {183-206},
publisher = {Seminario Matematico of the University of Padua},
title = {On Neumann's problem for a quasilinear differential system of the finite elastostatics type. Local theorems of existence and uniqueness},
url = {http://eudml.org/doc/107871},
volume = {68},
year = {1982},
}

TY - JOUR
AU - Lanza De Cristoforis, M.
AU - Valent, T.
TI - On Neumann's problem for a quasilinear differential system of the finite elastostatics type. Local theorems of existence and uniqueness
JO - Rendiconti del Seminario Matematico della Università di Padova
PY - 1982
PB - Seminario Matematico of the University of Padua
VL - 68
SP - 183
EP - 206
LA - eng
KW - Neumann's problem; quasilinear differential system; elastostatics; existence; uniqueness; dead traction problem
UR - http://eudml.org/doc/107871
ER -

References

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  1. [1] A. Adams, Soboles Spaces, Academic Press, 1975. Zbl0314.46030
  2. [2] S. Agmon - A. DOUGLIS - L. NIRENBERG, Estimates near the boundary for solutions of elliptic partial differential equations satisfying general boundary conditions II, Comm. Pure and Appl. Mathematics, 17 (1964), pp. 35-92. Zbl0123.28706MR162050
  3. [3] F. Browder, Estimates and existence theorems for elliptic boundary value problems, Proc. Nat. Acad. Sc. U.S.A., 45 (1959), pp. 365-372. Zbl0093.29402MR132913
  4. [4] H. Cartan, Cours de calcul differentiel, Hermann, Paris, 1977. Zbl0923.58002MR223194
  5. [5] G. Fichera, Existence Theorems in Elasticity, Handbuch der Physik, Bd. VIA/2, Springer Verlag (1972). 
  6. [6] J. Gobert, Une inégalité fondamentale de la théorie de l'élasticité, Bull. Soc. Roy. Sci., Liège, 3-4 (1962), pp. 182-191. Zbl0112.38902MR133684
  7. [7] M.E. Gurtin - S. J. SPECTOR, On Stability and uniqueness in finite elasticity, Arch. Rational Mech. Anal., 70 (1979), pp. 153-165. Zbl0426.73038MR546633
  8. [8] J.L. Lions - E. MAGENES, Problemi ai limiti non omogenei (III), Annali della Scuola Norm. Sup., Pisa, XV (1961), pp. 39-101. MR146526
  9. [9] F. Stoppelli, Un teorema di esistenza ed unicità relativo alle equazioni dell'elastostatica isoterma per deformazioni finite, Ricerche Matematiche, 3 (1954), pp. 247-267. Zbl0058.39701MR74237
  10. [10] F. Stoppelli, Su un sistema di equazioni integro-differenziali interessante l'elastostatica, Ricerche Matematiche, 6 (1957), pp. 11-26. Zbl0117.18403MR91003
  11. [11] F. Stoppelli, Sull'esistenza di soluzioni delle equazioni dell'elastostatica isoterma nel caso di sollecitazioni dotate di assi di equilibrio I, II, III, Ricerche Matematiche, 6 (1957), pp. 241-287; 7 (1958), pp. 71-101, 138-152. Zbl0097.17301
  12. [12] J.L. Thompson, Some existence theorems for the traction boundary value problem of linearized elastostatics, Arch. Rational Mech. Anal., 45 (1968), pp. 369-399. Zbl0175.22108MR237130
  13. [13] T. Valent - G. ZAMPIERI, Sulla differenziabilità di un operatore legato a una classe di sistemi differenziali quasi lineari, Rend. Sem. Mat. Univ. Padova, 57 (1977), pp. 311-322. Zbl0402.35027MR526198
  14. [14] T. Valent, Teoremi di esistenza e unicità in elastostatica finita, Rend. Sem. Mat. Univ. Padova60, (1979), pp. 165-181. Zbl0425.73011
  15. [15] T. Valent, Local existence and uniqueness theorems in finite elastostatics, Proceeding of the IUTAM symposium on finite elasticity, ed. Carlson and Shield, Martinus Nijhoff Publishers, the Hague - Boston - London, 1982. MR676677

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