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All issues Volume 58 / No 3 (May-June 2024) ESAIM: M2AN, 58 3 (2024) 993-1029 References
Open Access
Issue
ESAIM: M2AN
Volume 58, Number 3, May-June 2024
Page(s) 993 - 1029
DOI https://doi.org/10.1051/m2an/2024025
Published online 10 June 2024
  1. G. Alberti, S. Bianchini and G. Crippa, Structure of level sets and Sard-type properties of Lipschitz maps. Ann. Sc. Norm. Super. Pisa Cl. Sci. 12 (2013) 863–902. [MathSciNet] [Google Scholar]
  2. A. Bejan, Convection Heat Transfer, 4th edition. J. Wiley & Sons (2013). [CrossRef] [Google Scholar]
  3. J. Bourgain, M.V. Korobkov and J. Kristensen, On the Morse–Sard property and level sets of Sobolev and BV functions. Rev. Mat. Iberoam. 29 (2013) 1–23. [CrossRef] [MathSciNet] [Google Scholar]
  4. N.L. Carothers, Real Analysis. Cambridge University Press, Cambridge (2000). [CrossRef] [Google Scholar]
  5. E. Casas and F. Tröltzsch, Numerical analysis of some optimal control problems governed by a class of quasilinear elliptic equations. ESAIM:COCV 17 (2011) 771–800. [CrossRef] [EDP Sciences] [Google Scholar]
  6. E. Casas and F. Tröltzsch, A general theorem on error estimates with application to a quasilinear elliptic optimal control problem. Comput. Optim. Appl. 53 (2012) 173–206. [CrossRef] [MathSciNet] [Google Scholar]
  7. E. Casas and V. Dhamo, Error estimates for the numerical approximation of Neumann control problems governed by a class of quasilinear elliptic equations. Comput. Optim. Appl. 52 (2012) 719–756. [CrossRef] [MathSciNet] [Google Scholar]
  8. C. Christof and G. Wachsmuth, No-gap second-order conditions via a directional curvature functional. SIAM J. Optim. 28 (2018) 2097–2130. [CrossRef] [MathSciNet] [Google Scholar]
  9. C. Clason, V.H. Nhu, and A. Rösch, No-gap second-order optimality conditions for optimal control of a non-smooth quasilinear elliptic equation. ESAIM: COCV 27 (2021) 62. [CrossRef] [EDP Sciences] [Google Scholar]
  10. G.-H. Cottet and E. Maitre, A level set method for fluid-structure interactions with immersed surfaces. Math. Models Methods Appl. Sci. 16 (2006) 415–438. [CrossRef] [MathSciNet] [Google Scholar]
  11. K. Deckelnick and M. Hinze, A note on the approximation of elliptic control problems with bang-bang controls. Comput. Optim. Appl. 51 (2012) 931–939. [CrossRef] [MathSciNet] [Google Scholar]
  12. L.C. Evans and R.F. Gariepy, Measure Theory and Fine Properties of Function, 4th edition. CRC Press, New York (1992). [Google Scholar]
  13. A. Figalli, A simple proof of the Morse–Sard theorem in Sobolev spaces. Proc. Am. Math. Soc. 136 (2008) 3675–3681. [CrossRef] [Google Scholar]
  14. D. Gilbarg and N.S. Trudinger, Elliptic Partial Differential Equations of Second Order. Springer-Verlag, Berlin, Heidelberg (2001). [Google Scholar]
  15. P. Grisvard, Elliptic Problems in Nonsmooth Domains. Pitman Advanced Pub., Program (1985). [Google Scholar]
  16. V. Guillemin and A. Pollack, Differential Topology. American Mathematical Society, Providence, RI (1974). [Google Scholar]
  17. G. Leoni, A First Course in Sobolev Spaces, 2nd edition. American Mathematical Society, Providence, RI (2017). [CrossRef] [Google Scholar]
  18. J. Milnor, Topology from the Differentiable Viewpoint. University of Virginia Press (1965). [Google Scholar]
  19. V.H. Nhu, On the no-gap second-order optimality conditions for a non-smooth semilinear elliptic optimal control. Optimization 71 (2022) 4289–4319. [CrossRef] [MathSciNet] [Google Scholar]
  20. S. Osher and J.A. Sethian, Fronts propagating with curvature-dependent speed: Algorithms based on Hamilton–Jacobi formulations. J. Comput. Phys. 79 (1988) 12–49. [NASA ADS] [CrossRef] [Google Scholar]
  21. W. Rudin, Principles of Mathematical Analysis, 3rd edition. Mc Graw Hill Inc., New York (1976). [Google Scholar]
  22. A. Sard, The measure of the critical values of differentiable maps. Bull. Amer. Math. Soc. 48 (1942) 883–890. [CrossRef] [MathSciNet] [Google Scholar]
  23. J.A. Sethian, Curvature and the evolution of fronts. Commun. Math. Phys. 101 (1985) 487–499. [CrossRef] [Google Scholar]
  24. D. Wachsmuth and G. Wachsmuth, Second-order conditions for non-uniformly convex integrands: quadratic growth in L1. J. Nonsmooth Anal. Optim. 3 (2022) 8733. [CrossRef] [Google Scholar]
  25. Y.B. Zel’dovich and Y.P. Raizer, Physics of Shock Waves and High-Temperature Hydrodynamic Phenomena. Academic Press (1966). [Google Scholar]

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