Geodesic
Estimates near the boundary for second order derivatives of solutions of the Dirichlet problem for the biharmonic equation
Atti della Accademia nazionale dei Lincei. Rendiconti della Classe di scienze fisiche, matematiche e naturali, Série 8, Tome 80 (1986) no. 7-12, pp. 525-529.

Voir la notice de l'article provenant de la source Biblioteca Digitale Italiana di Matematica

Per ogni soluzione della (1) nel dominio limitato $\Omega$,, appartenente a $H_{0}^{2}(\Omega)$ e soddisfacente le condizioni (2), si dimostra la maggiorazione (5), valida nell'intorno di ogni punto $x^{0}$ del contorno; si consente a $\partial\Omega$ di essere singolare in $x^{0}$. 
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     title = {Estimates near the boundary for second order derivatives of solutions of the {Dirichlet} problem for the biharmonic equation},
     journal = {Atti della Accademia nazionale dei Lincei. Rendiconti della Classe di scienze fisiche, matematiche e naturali},
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Kondratiev, Vladimir A.; Oleinik, Olga A. Estimates near the boundary for second order derivatives of solutions of the Dirichlet problem for the biharmonic equation. Atti della Accademia nazionale dei Lincei. Rendiconti della Classe di scienze fisiche, matematiche e naturali, Série 8, Tome 80 (1986) no. 7-12, pp. 525-529. http://geodesic.mathdoc.fr/item/RLINA_1986_8_80_7-12_a4/

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[2] Kondratiev V.A., Kopacek J., Lekveishvili D.M. and Oleinik O.A. - Best possible estimates in Hölder spaces and the precise Saint-Venant principle for solutions of the biharmonic equation, «Trudy Mat. Institute im. Steklov», 166, 91-106, 1984. | MR | Zbl

[3] Kondratiev V.A. and Oleinik O.A. - On the smoothness of weak solutions of the Dirichlet problem for the biharmonic equation in domains with non-regular boundary. In: Nonlinear partial differential equations and their applications. College de France seminar, 7, 180-199, 1986. | MR | Zbl

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[5] Kopacek J. and Oleinik O.A. - On the behaviour of solutions of the elasticity system in a neighbourhood of irregular points of the boundary and at the infinity, «Transactions of the Moscow Math. Society», 43, 1981. | Zbl

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