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Exhausters, coexhausters and converters in nonsmooth analysis
Remarks on certain singular perturbations with illposed limit in shell theory and elasticity
1.  IMT, Université Paul Sabatier, 118, route de Narbonne, Toulouse, 31062, France 
2.  Laboratoire de Modélisation en Mécanique, Université Pierre et Marie Curie 4, place Jussieu, Paris, 75252, France 
References:
[1] 
S. Agmon, A. Douglis and L. Nirenberg, Estimates near the boundary for solutions of elliptic partial differential equations satisfying general boundary conditions. I., Comm. Pure. Applied Math., 12 (1959), 623727. doi: 10.1002/cpa.3160120405. 
[2] 
F. Béchet, O. Millet and E. SanchezPalencia, Singular perturbations generating complexification phenomena in elliptic shells, Comput. Mech., 43 (2008), 207221. 
[3] 
R. Courant and D. Hilbert, "Methods of Mathematical Physics. Vol. II: Partial Differential Equations," Interscience Publishers, New YorkLondon, 1962. 
[4] 
Yu. V. Egorov and V. A. Kondratév, The oblique derivative problem, Matem. sbornik (N.S.), 78 (1969), 148176. 
[5] 
Yu. V. Egorov, N. Meunier and E. SanchezPalencia, Rigorous and heuristic treatment of certain sensitive singular perturbations, Journal Math. Pures et Appliques (9), 88 (2007), 123147. doi: 10.1016/j.matpur.2007.04.010. 
[6] 
Yu. V. Egorov, N. Meunier and E. SanchezPalencia, "Rigorous and Heuristic Treatment of Sensitive Singular Perturbations Arising in Elliptic Shells," Around the research of V. Maz'ya, II, Int. Math. Ser. (N.Y.), 12, Springer, New York, (2010), 159202. 
[7] 
Yu. V. Egorov and M. A. Shubin, "Foundations of the Classical Theory of Partial Differential Equations," Reprint of the original English edition from the series Encyclopaedia of Mathematical Sciences, SpringerVerlag, Berlin, 1998. 
[8] 
J. Hadamard, "Lectures on Cauchy's Problem for Linear Partial Differential Equations," Dover, 1952. 
[9] 
P. R. Popivanov and D. K. Palagachev, "The Degenerate Oblique Derivative Problem for Elliptic and Parabolic Equations," Mathematical Research, 93, Akademie Verlag, Berlin, 1997. 
[10] 
L. Schwartz, "Théorie des Distributions," Hermann, Paris, 1961. 
[11] 
M. E. Taylor, "Pseudodifferential Operators," Princeton Mathematical Series, 34, Princeton University Press, Princeton, N.J., 1981. 
show all references
References:
[1] 
S. Agmon, A. Douglis and L. Nirenberg, Estimates near the boundary for solutions of elliptic partial differential equations satisfying general boundary conditions. I., Comm. Pure. Applied Math., 12 (1959), 623727. doi: 10.1002/cpa.3160120405. 
[2] 
F. Béchet, O. Millet and E. SanchezPalencia, Singular perturbations generating complexification phenomena in elliptic shells, Comput. Mech., 43 (2008), 207221. 
[3] 
R. Courant and D. Hilbert, "Methods of Mathematical Physics. Vol. II: Partial Differential Equations," Interscience Publishers, New YorkLondon, 1962. 
[4] 
Yu. V. Egorov and V. A. Kondratév, The oblique derivative problem, Matem. sbornik (N.S.), 78 (1969), 148176. 
[5] 
Yu. V. Egorov, N. Meunier and E. SanchezPalencia, Rigorous and heuristic treatment of certain sensitive singular perturbations, Journal Math. Pures et Appliques (9), 88 (2007), 123147. doi: 10.1016/j.matpur.2007.04.010. 
[6] 
Yu. V. Egorov, N. Meunier and E. SanchezPalencia, "Rigorous and Heuristic Treatment of Sensitive Singular Perturbations Arising in Elliptic Shells," Around the research of V. Maz'ya, II, Int. Math. Ser. (N.Y.), 12, Springer, New York, (2010), 159202. 
[7] 
Yu. V. Egorov and M. A. Shubin, "Foundations of the Classical Theory of Partial Differential Equations," Reprint of the original English edition from the series Encyclopaedia of Mathematical Sciences, SpringerVerlag, Berlin, 1998. 
[8] 
J. Hadamard, "Lectures on Cauchy's Problem for Linear Partial Differential Equations," Dover, 1952. 
[9] 
P. R. Popivanov and D. K. Palagachev, "The Degenerate Oblique Derivative Problem for Elliptic and Parabolic Equations," Mathematical Research, 93, Akademie Verlag, Berlin, 1997. 
[10] 
L. Schwartz, "Théorie des Distributions," Hermann, Paris, 1961. 
[11] 
M. E. Taylor, "Pseudodifferential Operators," Princeton Mathematical Series, 34, Princeton University Press, Princeton, N.J., 1981. 
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