Zacytuj

Amstutz, S. (2006). Topological sensitivity analysis for some nonlinear PDE system, Journal Mathematiques Pures et Appliquées 85(4): 540-557.10.1016/j.matpur.2005.10.008Search in Google Scholar

Bucur, D. and Buttazzo, G. (2005). Variational Methods in Shape Optimization Problems, Birkhäuser, Boston, MA.10.1007/b137163Search in Google Scholar

Casas, E. and Mateos, M. (2002). Uniform convergence of the FEM. Applications to state constrained control problems, Journal of Computational and Applied Mathematics 21(1): 67-100.Search in Google Scholar

Ciarlet, P. G. (1978). The Finite Element Method for Elliptic Problems, North-Holland, Amsterdam.10.1115/1.3424474Search in Google Scholar

Ciarlet, P. G. and Raviart, P. A. (1972). General Lagrange and Hermite interpolation in with applications to finite element methods, Archive for Rational Mechanics and Analysis 46(3): 177-199.10.1007/BF00252458Search in Google Scholar

Demlov, A. (2007). Sharply localized pointwise and W-1∞ estimates for finite element methods for quasilinear problems, Mathematics of Computation 76(260): 1725-1741.10.1090/S0025-5718-07-01983-7Search in Google Scholar

Frehse, J. and Rannacher, R. (1978). Asymptotic L∞-error estimates for linear finite element approximations of quasilinear boundary value problems, SIAM Journal on Numerical Analysis 15(2): 418-431.10.1137/0715026Search in Google Scholar

Fulmanski, P., Lauraine, A., Scheid, J.-F. and Sokołowski, J. (2007). A level set method in shape and topology optimization for variational inequalities, International Journal of Applied Mathematics and Computer Science 17(3): 413-430.10.2478/v10006-007-0034-zSearch in Google Scholar

Gilbarg, D. and Trudinger, N. S. (2001). Elliptic Partial Differential Equations of Second Order, Springer-Verlag, Berlin.10.1007/978-3-642-61798-0Search in Google Scholar

Haug, E. J. and Céa, J. (1981). Optimization of distributed parameter structures, Proceedings of the NATO Advanced Study Institute on Optimization of Distributed Parameter Structural Systems, Iowa City, IO, USA, NATO Advanced Study Institute Series E: Applied Sciences, Vol. 49, Martinus Nijhoff Publishers, The Hague.Search in Google Scholar

Il'in, A. M. (1989). Matching of Asymptotic Expansions of Solutions of Boundary Value Problems, Nauka, Moscow, (in Russian).Search in Google Scholar

Jackowska-Strumillo, L., Sokołowski, J., Zochowski, A. and Henrot, A. (2002). On numerical solution of shape inverse problems, Computational Optimization and Applications 23(2): 231-255.10.1023/A:1020528902875Search in Google Scholar

Kondratiev, V. A. (1967). Boundary problems for elliptic equations in domains with conical or angular points, Trudy Moskovskogo Matematicheskogo Obszhestva 16: 209-292, (in Russian).Search in Google Scholar

Ladyzhenskaya, O. A. and Ural'tseva, N. N. (1968). Linear and Quasilinear Elliptic Equations, Academic Press, New York, NY London.Search in Google Scholar

Landkof, N. S. (1966). Fundamentals of Modern Potential Theory, Nauka, Moscow, (in Russian).Search in Google Scholar

Mazja, V. G., Nazarov, S. A. and Plamenevskii, B. A. (1981). On the asymptotic behavior of solutions of elliptic boundary value problems with irregular perturbations of the domain, Problemy Matematicheskogo Analiza 8: 72-153.Search in Google Scholar

Mazja, V. G., Nazarov, S. A. and Plamenevskii, B. A. (1991). Asymptotische Theorie elliptischer Randwertaufgaben in singulär gestörten, Gebieten. Bd. 1, Akademie-Verlag, Berlin; English translation: Asymptotic Theory of Elliptic Boundary Value Problems in Singularly Perturbed Domains, Vol. 1, Birkäuser Verlag, Basel, 2000.Search in Google Scholar

Mazja, V. G. and Plamenevskii, B. A. (1978). Estimates in Lp and Hölder classes and the Miranda-Agmon maximum principle for solutions of elliptic boundary value problems in domains with singular points on the boundary, Matematische Nachrichten 81(1): 25-82, (in Russian).Search in Google Scholar

Mazja, V. G. and Plamenevskii, B. A. (1973). On the behavior of solutions to quasilinear elliptic boundary-value problems in a neighborhood of a conical point, Zapiski Nauchnych Seminarov Leningradskogo Otdeleniya Matematicheskogo Instituta (LOMI) 38: 91-97.Search in Google Scholar

Nazarov, S. A. and Plamenevsky, B. A. (1973). Elliptic Problems in Domains with Piecewise Smooth Boundaries, Walter de Gruyter, Berlin.Search in Google Scholar

Nazarov, S. A. and Sokolowski, J. (2006). Self-adjoint extensions for the Neumann Laplace and applications, Acta Mathematica Sinica 22(3): 879-906.10.1007/s10114-005-0652-zSearch in Google Scholar

Nazarov, S. A. and Sokolowski, J. (2003). Asymptotic analysis of shape functional, Journal de Mathématiques Pures et Appliquées 82(2): 125-196.10.1016/S0021-7824(03)00004-7Search in Google Scholar

Pólya, G. P. and Szegö, G. (1951). Isoperimetric Inequalities in Mathematical Physics, Princeton University Press, Princeton, NJ.10.1515/9781400882663Search in Google Scholar

Raviart, P. A. and Thomas, J.M. (1983). Introduction à l'analyse numérique des équations aux dérives partielles Masson, Paris.Search in Google Scholar

Sokolowski, J. and Zochowski, A. (1999). Asymptotic analysis of shape functional, Numerische Mathematik 102(1): 145-179.Search in Google Scholar

Sokolowski, J. and Zochowski, A. (2005). Introduction to Shape Optimization. Shape Sensitivity Analysis, Springer-Verlag, Berlin.Search in Google Scholar

Sokolowski, J. and Zochowski, A. (1999). On topological derivative in shape optimization, SIAM Journal on Control and Optimization 37(4): 1251-1272.10.1137/S0363012997323230Search in Google Scholar

Sokolowski, J. and Zochowski, A. (2003). Optimality conditions for simultaneous topology and shape optimization, SIAM Journal on Control and Optimization 42(4): 1198-1221.10.1137/S0363012901384430Search in Google Scholar

Sokolowski, J. and Zochowski, A. (2001). Topological derivatives of shape functional for elasticity systems, Mechanics of Structures and Machines 29(3): 331-349.10.1081/SME-100105654Search in Google Scholar

Sokolowski, J. and Zochowski, A. (1999). On topological derivative in shape optimization, SIAM Journal on Control and Optimization 37(4): 1251-1272.10.1137/S0363012997323230Search in Google Scholar

Stampacchia, G. (1965). Le problème de Dirichlet pour les équations elliptiques du second ordre à coefficients discontinus, Annales de I'Institut Fourier 15: 189-258.10.5802/aif.204Search in Google Scholar

ISSN:
1641-876X
Język:
Angielski
Częstotliwość wydawania:
4 razy w roku
Dziedziny czasopisma:
Mathematics, Applied Mathematics