Free Access
Issue |
ESAIM: COCV
Volume 14, Number 3, July-September 2008
|
|
---|---|---|
Page(s) | 575 - 589 | |
DOI | https://doi.org/10.1051/cocv:2007063 | |
Published online | 21 December 2007 |
- N. Arada, E. Casas and F. Tröltzsch, Error estimates for the numerical approximation of a semilinear elliptic control problem. Comput. Optim. Appl. 23 (2002) 201–229. [CrossRef] [MathSciNet] [Google Scholar]
- J.F. Bonnans and E. Casas, Contrôle de systèmes elliptiques semilinéaires comportant des contraintes sur l'état, in Nonlinear Partial Differential Equations and Their Applications, Collège de France Seminar 8, H. Brezis and J.-L. Lions Eds., Longman Scientific & Technical, New York (1988) 69–86. [Google Scholar]
- E. Casas, Pontryagin's principle for optimal control problems governed by semilinear elliptic equations, in International Conference on Control and Estimation of Distributed Parameter Systems: Nonlinear Phenomena, F. Kappel and K. Kunisch Eds., Basel, Birkhäuser, Int. Series Num. Analysis. 118 (1994) 97–114. [Google Scholar]
- E. Casas, Error estimates for the numerical approximation of semilinear elliptic control problems with finitely many state constraints. ESAIM: COCV 8 (2002) 345–374. [CrossRef] [EDP Sciences] [Google Scholar]
- E. Casas and M. Mateos, Second order optimality conditions for semilinear elliptic control problems with finitely many state constraints. SIAM J. Control Optim. 40 (2002) 1431–1454. [CrossRef] [MathSciNet] [Google Scholar]
- E. Casas and M. Mateos, Uniform convergence of the FEM. Applications to state constrained control problems. Comp. Appl. Math. 21 (2002) 67–100. [Google Scholar]
- E. Casas and F. Tröltzsch, Second order necessary optimality conditions for some state-constrained control problems of semilinear elliptic equations. App. Math. Optim. 39 (1999) 211–227. [CrossRef] [Google Scholar]
- E. Casas and F. Tröltzsch, Second order necessary and sufficient optimality conditions for optimization problems and applications to control theory. SIAM J. Optim. 13 (2002) 406–431. [CrossRef] [MathSciNet] [Google Scholar]
- E. Casas, J.P. Raymond and H. Zidani, Optimal control problems governed by semilinear elliptic equations with integral control constraints and pointwise state constraints, in International Conference on Control and Estimations of Distributed Parameter Systems, W. Desch, F. Kappel and K. Kunisch Eds., Basel, Birkhäuser, Int. Series Num. Analysis. 126 (1998) 89–102. [Google Scholar]
- E. Casas, F. Tröltzsch and A. Unger, Second order sufficient optimality conditions for some state constrained control problems of semilinear elliptic equations. SIAM J. Control Optim. 38 (2000) 1369–1391. [Google Scholar]
- F.H. Clarke, A new approach to Lagrange multipliers. Math. Op. Res. 1 (1976) 165–174. [Google Scholar]
- P. Grisvard, Elliptic Problems in Nonsmooth Domains. Pitman, Boston-London-Melbourne (1985). [Google Scholar]
- E. Hewitt and K. Stromberg, Real and abstract analysis. Springer-Verlag, Berlin-Heidelberg-New York (1965). [Google Scholar]
- W. Littman and G. Stampacchia and H.F. Weinberger, Regular points for elliptic equations with discontinuous coefficients. Ann. Scuola Normale Sup. Pisa 17 (1963) 43–77. [Google Scholar]
- M. Mateos, Problemas de control óptimo gobernados por ecuaciones semilineales con restricciones de tipo integral sobre el gradiente del estado. Ph.D. thesis, University of Cantabria, Spain (2000). [Google Scholar]
- H. Maurer and J. Zowe, First- and second-order conditions in infinite-dimensional programming problems. Math. Program. 16 (2000) 431–450. [Google Scholar]
- J.-P. Raymond and F. Tröltzsch, Second order sufficient optimality conditions for nonlinear parabolic control problems with state constraints. Discrete Contin. Dynam. Systems 6 (1979) 98–110. [Google Scholar]
- S.M. Robinson, Stability theory for systems of inequalities, Part II: Differentiable nonlinear systems. SIAM J. Numer. Anal. 13 (1976) 497–513. [CrossRef] [MathSciNet] [Google Scholar]
- J.C. Saut and B. Scheurer, Sur l'unicité du problème de Cauchy et le prolongement unique pour des équations elliptiques à coefficients non localement bornés. J. Differential Equations 43 (1982) 28–43. [CrossRef] [MathSciNet] [Google Scholar]
Current usage metrics show cumulative count of Article Views (full-text article views including HTML views, PDF and ePub downloads, according to the available data) and Abstracts Views on Vision4Press platform.
Data correspond to usage on the plateform after 2015. The current usage metrics is available 48-96 hours after online publication and is updated daily on week days.
Initial download of the metrics may take a while.