Free access
Issue
ESAIM: COCV
Volume 15, Number 4, October-December 2009
Page(s) 782 - 809
DOI http://dx.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]
  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]
  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. [MathSciNet]
  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]
  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]
  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]
  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]
  8. P.G. Ciarlet, Basic error estimates for elliptic problems, in Handbook of Numerical Analysis II, North-Holland, Amsterdam (1991) 17–351.
  9. M. Costabel and M. Dauge, A singularly perturbed mixed boundary value problem. Comm. Partial Diff. Eq. 21 (1996) 1919–1949. [CrossRef]
  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]
  11. P. Grisvard, Elliptic Problems in Nonsmooth Domains. Pitman, Boston (1985).
  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]
  13. D. Jerison and C. Kenig, The Neumann problem on Lipschitz domains. Bull. Amer. Math. Soc. (N.S.) 4 (1981) 203–207. [CrossRef] [MathSciNet]
  14. D. Jerison and C.E. Kenig, The inhomogeneous Dirichlet problem in Lipschitz domains. J. Funct. Anal. 130 (1995) 161–219. [CrossRef] [MathSciNet]
  15. C.V. Pao, Nonlinear parabolic and elliptic equations. Plenum Press, New York (1992).
  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]
  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]