The role of ellipticity and normality assumptions in formulating live-boundary conditions in elasticity
Authors:
P. Podio-Guidugli, G. Vergara-Caffarelli and E. G. Virga
Journal:
Quart. Appl. Math. 44 (1987), 659-664
MSC:
Primary 73C50; Secondary 73C35
DOI:
https://doi.org/10.1090/qam/872818
MathSciNet review:
872818
Full-text PDF Free Access
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Additional Information
- Morton E. Gurtin and A. Ian Murdoch, A continuum theory of elastic material surfaces, Arch. Rational Mech. Anal. 57 (1975), 291–323. MR 371223, DOI https://doi.org/10.1007/BF00261375
- Scott J. Spector, On uniqueness in finite elasticity with general loading, J. Elasticity 10 (1980), no. 2, 145–161 (English, with French summary). MR 576164, DOI https://doi.org/10.1007/BF00044500
- Scott J. Spector, On uniqueness for the traction problem in finite elasticity, J. Elasticity 12 (1982), no. 4, 367–383. MR 685512, DOI https://doi.org/10.1007/BF00042210
- Morton E. Gurtin, On the nonlinear theory of elasticity, Contemporary developments in continuum mechanics and partial differential equations (Proc. Internat. Sympos., Inst. Mat., Univ. Fed. Rio de Janeiro, Rio de Jane, North-Holland Math. Stud., vol. 30, North-Holland, Amsterdam-New York, 1978, pp. 237–253. MR 519646
- Giuseppe Geymonat, Su alcuni problemi ai limiti per i sistemi lineari ellitici secondo Petrowsky, Matematiche (Catania) 20 (1965), 211–253 (Italian). MR 201817
- Gerd Grubb, Weakly semibounded boundary problems and sesquilinear forms, Ann. Inst. Fourier (Grenoble) 23 (1973), no. 4, 145–194 (English, with French summary). MR 344669
J. L. Lions and E. Magenes, Problèmes aux limites non homogènes, Dunod, Paris (1968)
P. Podio-Guidugli, G. Vergara Caffarelli and E. G. Virga, Una formula di Green per il problema di carichi vivi dell’elastostatica linearizzata, Atti VII Congr. AIMETA, Trieste, vol. 2, pp. 1–10 (2–5 October 1984)
P. Podio-Guidugli, G. Vergara Caffarelli and E. G. Virga, in preparation,
M. E. Gurtin, The linear theory of elasticity, in Handbuch der physik, vol. VIa/2 (C. Truesdell, ed.). Springer, Berlin (1972)
M. E. Gurtin and A. I. Murdoch, A continuum theory of elastic material surfaces, Arch. Rat. Mech. Anal. 57, 291–323 (1975)
S. J. Spector, On uniqueness in finite elasticity with general loading, J. Elasticity 10, 145–161 (1980)
S. J. Spector, On uniqueness for the traction problem in finite elasticity, J. Elasticity 12, 367–383 (1982)
M. E. Gurtin, On the non-linear theory of elasticity, in Contemporary developments in continuum mechanics and partial differential equations (G. M. de La Penha and L. A. J. Medeiros, eds., pp. 237–253, North Holland, Amsterdam (1978)
G. Geymonat, Su alcuni problemi ai limiti per i sistemi lineari ellittici secondo Petrowskii, Matematiche 20, 211–253 (1965)
G. Grubb, Weakly semibounded boundary problems and sesquilinear forms, Ann. Inst. Fourier Grenoble 23, 145–194 (1973)
J. L. Lions and E. Magenes, Problèmes aux limites non homogènes, Dunod, Paris (1968)
P. Podio-Guidugli, G. Vergara Caffarelli and E. G. Virga, Una formula di Green per il problema di carichi vivi dell’elastostatica linearizzata, Atti VII Congr. AIMETA, Trieste, vol. 2, pp. 1–10 (2–5 October 1984)
P. Podio-Guidugli, G. Vergara Caffarelli and E. G. Virga, in preparation,
M. E. Gurtin, The linear theory of elasticity, in Handbuch der physik, vol. VIa/2 (C. Truesdell, ed.). Springer, Berlin (1972)
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© Copyright 1987
American Mathematical Society
