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Regularity in Campanato spaces for solutions of fully nonlinear elliptic systems
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Exhausters, coexhausters and converters in nonsmooth analysis
Remarks on certain singular perturbations with ill-posed 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), 623-727.
doi: 10.1002/cpa.3160120405. |
[2] |
F. Béchet, O. Millet and E. Sanchez-Palencia, Singular perturbations generating complexification phenomena in elliptic shells, Comput. Mech., 43 (2008), 207-221. |
[3] |
R. Courant and D. Hilbert, "Methods of Mathematical Physics. Vol. II: Partial Differential Equations," Interscience Publishers, New York-London, 1962. |
[4] |
Yu. V. Egorov and V. A. Kondratév, The oblique derivative problem, Matem. sbornik (N.S.), 78 (1969), 148-176. |
[5] |
Yu. V. Egorov, N. Meunier and E. Sanchez-Palencia, Rigorous and heuristic treatment of certain sensitive singular perturbations, Journal Math. Pures et Appliques (9), 88 (2007), 123-147.
doi: 10.1016/j.matpur.2007.04.010. |
[6] |
Yu. V. Egorov, N. Meunier and E. Sanchez-Palencia, "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), 159-202. |
[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, Springer-Verlag, 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), 623-727.
doi: 10.1002/cpa.3160120405. |
[2] |
F. Béchet, O. Millet and E. Sanchez-Palencia, Singular perturbations generating complexification phenomena in elliptic shells, Comput. Mech., 43 (2008), 207-221. |
[3] |
R. Courant and D. Hilbert, "Methods of Mathematical Physics. Vol. II: Partial Differential Equations," Interscience Publishers, New York-London, 1962. |
[4] |
Yu. V. Egorov and V. A. Kondratév, The oblique derivative problem, Matem. sbornik (N.S.), 78 (1969), 148-176. |
[5] |
Yu. V. Egorov, N. Meunier and E. Sanchez-Palencia, Rigorous and heuristic treatment of certain sensitive singular perturbations, Journal Math. Pures et Appliques (9), 88 (2007), 123-147.
doi: 10.1016/j.matpur.2007.04.010. |
[6] |
Yu. V. Egorov, N. Meunier and E. Sanchez-Palencia, "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), 159-202. |
[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, Springer-Verlag, 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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