Free Access
Issue
ESAIM: COCV
Volume 15, Number 4, October-December 2009
Page(s) 782 - 809
DOI https://doi.org/10.1051/cocv:2008049
Published online 20 August 2008
  1. J.-J. Alibert and J.-P. Raymond, Boundary control of semilinear elliptic equations with discontinuous leading coefficients and unbounded controls. Numer. Funct. Anal. Optim. 18 (1997) 235–250. [CrossRef] [MathSciNet] [Google Scholar]
  2. F. Ben Belgacem, H. El Fekih and H. Metoui, Singular perturbation for the Dirichlet boundary control of elliptic problems. ESAIM: M2AN 37 (2003) 833–850. [CrossRef] [EDP Sciences] [Google Scholar]
  3. F. Ben Belgacem, H. El Fekih and J.-P. Raymond, A penalized Robin approach for solving a parabolic equation with nonsmooth Dirichlet boundary conditions. Asymptot. Anal. 34 (2003) 121–136. [EDP Sciences] [MathSciNet] [Google Scholar]
  4. E. Casas and M. Mateos, Error estimates for the numerical approximation of Neumann control problems. Comput. Optim. Appl. 39 (2008) 265–295. [CrossRef] [MathSciNet] [Google Scholar]
  5. E. Casas and J.-P. Raymond, Error estimates for the numerical approximation of Dirichlet boundary control for semilinear elliptic equations. SIAM J. Contr. Opt. 45 (2006) 1586–1611 (electronic). [CrossRef] [MathSciNet] [Google Scholar]
  6. E. Casas and J.-P. Raymond, The stability in Formula spaces of Formula -projections on some convex sets. Numer. Funct. Anal. Optim. 27 (2006) 117–137. [CrossRef] [MathSciNet] [Google Scholar]
  7. E. Casas, M. Mateos and F. Tröltzsch, Error estimates for the numerical approximation of boundary semilinear elliptic control problems. Comput. Optim. Appl. 31 (2005) 193–219. [CrossRef] [MathSciNet] [Google Scholar]
  8. P.G. Ciarlet, Basic error estimates for elliptic problems, in Handbook of Numerical Analysis II, North-Holland, Amsterdam (1991) 17–351. [Google Scholar]
  9. M. Costabel and M. Dauge, A singularly perturbed mixed boundary value problem. Comm. Partial Diff. Eq. 21 (1996) 1919–1949. [CrossRef] [Google Scholar]
  10. Z. Ding, A proof of the trace theorem of Sobolev spaces on Lipschitz domains. Proc. Amer. Math. Soc. 124 (1996) 591–600. [CrossRef] [MathSciNet] [Google Scholar]
  11. P. Grisvard, Elliptic Problems in Nonsmooth Domains. Pitman, Boston (1985). [Google Scholar]
  12. L.S. Hou and S.S. Ravindran, A penalized Neumann control approach for solving an optimal Dirichlet control problem for the Navier-Stokes equations. SIAM J. Contr. Opt. 36 (1998) 1795–1814 (electronic). [CrossRef] [MathSciNet] [Google Scholar]
  13. D. Jerison and C. Kenig, The Neumann problem on Lipschitz domains. Bull. Amer. Math. Soc. (N.S.) 4 (1981) 203–207. [CrossRef] [MathSciNet] [Google Scholar]
  14. D. Jerison and C.E. Kenig, The inhomogeneous Dirichlet problem in Lipschitz domains. J. Funct. Anal. 130 (1995) 161–219. [CrossRef] [MathSciNet] [Google Scholar]
  15. C.V. Pao, Nonlinear parabolic and elliptic equations. Plenum Press, New York (1992). [Google Scholar]
  16. J.-P. Raymond, Stokes and Navier-Stokes equations with nonhomogeneous conditions. Ann. Inst. H. Poincaré Anal. Non Linéaire 24 (2007) 921–951. [CrossRef] [MathSciNet] [Google Scholar]
  17. G. Stampacchia, Le problème de Dirichlet pour les équations elliptiques du second ordre à coefficients discontinus. Ann. Inst. Fourier (Grenoble) 15 (1965) 189–258. [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.