Free Access
Volume 22, Number 2, April-June 2016
Page(s) 355 - 370
Published online 04 March 2016
  1. L. Boccardo and T. Gallouet, Non-linear elliptic and parabolic equations involving measure data. J. Funct. Anal. 87 (1989) 149–169. [CrossRef] [MathSciNet] [Google Scholar]
  2. E. Casas, Pontryagin’s principle for state-constrained boundary control problems of semilinear parabolic equations. SIAM J. Control Optim. 35 (1997) 1297–1327. [CrossRef] [MathSciNet] [Google Scholar]
  3. E. Casas and K. Kunisch, Optimal control of semilinear elliptic equations in measure spaces. SIAM J. Control Optim. 52 (2013) 339–364. [Google Scholar]
  4. E. Casas and E. Zuazua, Spike controls for elliptic and parabolic pde. Systems Control Lett. 62 (2013) 311–318. [CrossRef] [MathSciNet] [Google Scholar]
  5. E. Casas, C. Clason and K. Kunisch, Approximation of elliptic control problems in measure spaces with sparse solutions. SIAM J. Control Optim. 50 (2012) 1735–1752. [CrossRef] [MathSciNet] [Google Scholar]
  6. E. Casas, C. Clason and K. Kunisch, Parabolic control problems in measure spaces with sparse solutions. SIAM J. Control Optim. 51 (2013) 28–63. [CrossRef] [MathSciNet] [Google Scholar]
  7. P.G. Ciarlet and J.L. Lions, Handbook of Numerical Analysis: II. Handbook of Numerical Analysis. North-Holland (1990). [Google Scholar]
  8. C. Clason and K. Kunisch, A duality-based approach to elliptic control problems in non-reflexive Banach spaces. ESAIM: COCV 17 (2011) 243–266. [CrossRef] [EDP Sciences] [Google Scholar]
  9. E. Di Benedetto, On the local behaviour of solutions of degenerate parabolic equations with measurable coefficients. Annali della Scuola Normale Superiore di Pisa − Classe di Scienze13 (1986) 487–535. [Google Scholar]
  10. L.C. Evans, Partial Differential Equations. Grad. Stud. Math. American Mathematical Society (2010). [Google Scholar]
  11. P. Grisvard, Elliptic Problems in Nonsmooth Domains. Classics Appl. Math. Society for Industrial and Applied Mathematics (1985). [Google Scholar]
  12. R. Herzog and G. Stadler and G. Wachsmuth, Directional sparsity in optimal control of partial differential equations. SIAM J. Control Optim. 50 (2012) 943–963. [Google Scholar]
  13. K. Kunisch, K. Pieper and B. Vexler, Measure valued directional sparsity for parabolic optimal control problems. SIAM J. Control Optim. 52 (2014) 3078–3108. [CrossRef] [MathSciNet] [Google Scholar]
  14. O.A. Ladyzhenskaia, V.A. Solonnikov and N.N. Uralceva, Linear and Quasi-linear Equations of Parabolic Type. American Mathematical Society, Translations of Mathematical Monographs. American Mathematical Society (1968). [Google Scholar]
  15. Y. Li, S. Osher and R. Tsai, Heat source identification based on l1 constrained minimization. Inverse Probl. Imaging 8 (2014) 199–221. [CrossRef] [MathSciNet] [Google Scholar]
  16. K. Pieper and B. Vexler, A priori error analysis for discretization of sparse elliptic optimal control problems in measure space. SIAM J. Control Optim. 51 (2013) 2788–2808. [CrossRef] [MathSciNet] [Google Scholar]
  17. J.P. Raymond and H. Zidani, Hamiltonian pontryagin’s principles for control problems governed by semilinear parabolic equations. Appl. Math. Optim. 39 (1999) 143–177. [CrossRef] [MathSciNet] [Google Scholar]
  18. A.H. Schatz, Pointwise error estimates and asymptotic error expansion inequalities for the finite element method on irregular grids. Part I. Global Estimates. Math. Comput. 67 (1998) 877–899. [CrossRef] [Google Scholar]
  19. J. Simon, Compact sets in the space Lp(O,T;B). Ann. Mat. Pura Appl. 146 (1986) 65–96. [Google Scholar]
  20. V. Thomée, Galerkin Finite Element Methods for Parabolic Problems. Springer Ser. Comput. Math. Springer-Verlag New York, Inc., Secaucus, NJ, USA (2006). [Google Scholar]
  21. N. Walkington, Compactness properties of the dg and cg time stepping schemes for parabolic equations. SIAM J. Numer. Anal. 47 (2010) 4680–4710. [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.