Remarks about Signorini's problem in linear elasticity

David Kinderlehrer

Annali della Scuola Normale Superiore di Pisa - Classe di Scienze (1981)

  • Volume: 8, Issue: 4, page 605-645
  • ISSN: 0391-173X

How to cite

top

Kinderlehrer, David. "Remarks about Signorini's problem in linear elasticity." Annali della Scuola Normale Superiore di Pisa - Classe di Scienze 8.4 (1981): 605-645. <http://eudml.org/doc/83870>.

@article{Kinderlehrer1981,
author = {Kinderlehrer, David},
journal = {Annali della Scuola Normale Superiore di Pisa - Classe di Scienze},
keywords = {connectedness conditions; plane elastostatics; displacement vector is continuous; continuously differentiable},
language = {eng},
number = {4},
pages = {605-645},
publisher = {Scuola normale superiore},
title = {Remarks about Signorini's problem in linear elasticity},
url = {http://eudml.org/doc/83870},
volume = {8},
year = {1981},
}

TY - JOUR
AU - Kinderlehrer, David
TI - Remarks about Signorini's problem in linear elasticity
JO - Annali della Scuola Normale Superiore di Pisa - Classe di Scienze
PY - 1981
PB - Scuola normale superiore
VL - 8
IS - 4
SP - 605
EP - 645
LA - eng
KW - connectedness conditions; plane elastostatics; displacement vector is continuous; continuously differentiable
UR - http://eudml.org/doc/83870
ER -

References

top
  1. [1] S. Agmon - A. Douglis - L. Nirenberg, Estimates near the boundary for solutions of elliptic partial differential equations satisfying general conditions, II, Comm. Pure Appl. Math., 22 (1964), pp. 35-92. Zbl0123.28706MR162050
  2. [2] S. Campanato, Proprietà di holderianità di alcune classi di funzioni, Ann. Scuola Norm. Sup.Pisa, 17 (1963), pp. 175-188. Zbl0121.29201MR156188
  3. [3] G. Duvaut - J.L. Lions, Les inéquations en méchanique et en physique, Dunod, Paris (1972). Zbl0298.73001MR464857
  4. [4] G. Fichera, Problemi elastostatici con vincoli unilaterali : il problema di Signorini con ambigue condizioni al contorno, Atti Accad. Naz. Lincei, 8 (1963 -1964), pp. 91-140. Zbl0146.21204MR178631
  5. [5] D.G. De Figueiredo, The coerciveness problem for forms over vector valued functions, Comm. Pure Appl. Math., 16 (1963), pp. 63-94. Zbl0136.09502MR149082
  6. [6] J. Frehse, Two dimensional variational problems with thin obstacles, Math. Z., 143 (1975), pp. 279-288. Zbl0295.49003MR380550
  7. [7] F. Gehring, The Lp integrability of the partial derivatives of a quasi-conformal mapping, Acta Math., 130 (1973), pp. 265-277. Zbl0258.30021MR402038
  8. [8] M. Giaquinta - G. Modica, Regularity results for some classes of higher order non linear elliptic systems, J. Reine Angew. Math., 311 (1979), pp. 145-169. Zbl0409.35015MR549962
  9. [9] S. Hildebrandt - K.-O. Widman, Some regularity results for quasi-linear elliptic systems of second order, Math. Z., 142 (1975), pp. 67-86. Zbl0317.35040MR377273
  10. [10] J.J. Kalker, Aspects of contact mechanics, in Proc. of Int. Union of Theoretical and Appl. Mech. (Pater and Kalker, eds.), Delft. Univ. Press (1975), pp. 1-25. Zbl0318.73016MR445987
  11. [11] D. Kindfrlehrer, The smoothness of the solution of the boundary obstacle problem, J. Math. Pures Appl.60 (1981) pp. 193-212. Zbl0459.35092MR620584
  12. [12] D. Kinderlehrer - G. Stampacchia, An introduction to variational inequalities and their applications, Academic Press, New York (1980). Zbl0457.35001MR567696
  13. [13] R.J. Knops - L.E. Payne, Uniqueness theorems in elasticity, Spring, New York, Heidelberg-Berlin (1971). Zbl0224.73016MR421244
  14. [14] H. Lewy, On a variational problem with inequalities on the boundary, Indiana J. Math., 17 (1968), pp. 861-884. Zbl0153.43303MR222734
  15. [15] H. Lewy, On the coincidence set in variational inequalities, J. Differential Geometry, 6 (1972), pp. 497-501. Zbl0255.31002MR320343
  16. [16] J.L. Lions - G. Stampacchia, Variational inequalities, Comm. Pure Appl. Math., 20 (1967), pp. 493-519. Zbl0152.34601MR216344
  17. [17] N.G. Meyers, An Lp estimate for the gradient of solutions of second order elliptic divergence equations, Ann. Scuola Norm. Sup. Pisa, 17 (1963), pp. 189-206. Zbl0127.31904MR159110
  18. [18] C.B. Morreyjr., Multiple integrals in the calculus of variations, Springer, New York (1966). Zbl0142.38701MR202511
  19. [19] N.I. Muskhelishvili, Singular Integral Equations, Noordhoff, Groningen (1953). Zbl0051.33203MR355494
  20. [20] N.I. Muskhelishvili, Some basic problems of the mathematical theory of elasticity, Noordhoff, Groningen (1953). Zbl0052.41402MR58417
  21. [21] L. Nirenberg, Remarks on strongly elliptic partial differential equations, Comm. Pure Appl. Math., 8 (1955), pp. 648-674. Zbl0067.07602MR75415
  22. [22] A. Signorini, Questioni di elasticità nonlinearizzata e semilinearizzata, Rend. Mat., 18 (1959). Zbl0091.38006MR118021
  23. [23] G. Stampacchia, Le problème de Dirichlet pour les équations elliptiques du second ordre à coefficients discontinus, Ann. Inst. Fourier Grenoble, 15 (1965), pp. 189-258. Zbl0151.15401MR192177
  24. [24] P. Villaggio, A unilateral contact problem in linear elasticity, J. Elasticity, 10 (1980), pp. 113-119. Zbl0425.73097MR576162
  25. [25] K.-O. Widman, Hölder continuity of elliptic systems, Manuscripta Math., 5 (1971), pp. 299-308. Zbl0223.35044MR296484

NotesEmbed ?

top

You must be logged in to post comments.

To embed these notes on your page include the following JavaScript code on your page where you want the notes to appear.

Only the controls for the widget will be shown in your chosen language. Notes will be shown in their authored language.

Tells the widget how many notes to show per page. You can cycle through additional notes using the next and previous controls.

    
                

Note: Best practice suggests putting the JavaScript code just before the closing </body> tag.