Regularity of the optimal shape for the first eigenvalue of the laplacian with volume and inclusion constraints

Tanguy Briançon; Jimmy Lamboley

Annales de l'I.H.P. Analyse non linéaire (2009)

  • Volume: 26, Issue: 4, page 1149-1163
  • ISSN: 0294-1449

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Briançon, Tanguy, and Lamboley, Jimmy. "Regularity of the optimal shape for the first eigenvalue of the laplacian with volume and inclusion constraints." Annales de l'I.H.P. Analyse non linéaire 26.4 (2009): 1149-1163. <http://eudml.org/doc/78883>.

@article{Briançon2009,
author = {Briançon, Tanguy, Lamboley, Jimmy},
journal = {Annales de l'I.H.P. Analyse non linéaire},
keywords = {shape optimization; eigenvalues of the Laplace operator; regularity of free boundaries},
language = {eng},
number = {4},
pages = {1149-1163},
publisher = {Elsevier},
title = {Regularity of the optimal shape for the first eigenvalue of the laplacian with volume and inclusion constraints},
url = {http://eudml.org/doc/78883},
volume = {26},
year = {2009},
}

TY - JOUR
AU - Briançon, Tanguy
AU - Lamboley, Jimmy
TI - Regularity of the optimal shape for the first eigenvalue of the laplacian with volume and inclusion constraints
JO - Annales de l'I.H.P. Analyse non linéaire
PY - 2009
PB - Elsevier
VL - 26
IS - 4
SP - 1149
EP - 1163
LA - eng
KW - shape optimization; eigenvalues of the Laplace operator; regularity of free boundaries
UR - http://eudml.org/doc/78883
ER -

References

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  2. [2] Alt H.W., Caffarelli L.A., Friedman A., Variational problems with two phases and their free boundaries, Trans. Amer. Math. Soc.282 (2) (1984) 431-461. Zbl0844.35137MR732100
  3. [3] Briançon T., Regularity of optimal shapes for the Dirichlet's energy with volume constraint, ESAIM: COCV10 (2004) 99-122. Zbl1118.35078MR2084257
  4. [4] Briançon T., Hayouni M., Pierre M., Lipschitz continuity of state functions in some optimal shaping, Calc. Var. Partial Differential Equations23 (1) (2005) 13-32. Zbl1062.49035MR2133659
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  6. [6] Caffarelli L.A., Jerison D., Kenig C.E., Global energy minimizers for free boundary problems and full regularity in three dimensions, in: Contemp. Math., vol. 350, Amer. Math. Soc., Providence, RI, 2004, pp. 83-97. Zbl1330.35545MR2082392
  7. [7] Crouzeix M., Variational approach of a magnetic shaping problem, Eur. J. Mech. B/Fluids10 (1991) 527-536. Zbl0741.76089MR1139607
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  9. [9] Evans L.C., Gariepy R.F., Measure Theory and Fine Properties of Functions, Studies in Advanced Mathematics, CRC Press, Boca Raton, FL, 1992. Zbl0804.28001MR1158660
  10. [10] Giusti E., Minimal Surfaces and Functions of Bounded Variation, Monographs in Mathematics, vol. 80, Birkhäuser Verlag, Basel–Boston, MA, 1984. Zbl0545.49018MR775682
  11. [11] Gustafsson B., Shahgholian H., Existence and geometric properties of solutions of a free boundary problem in potential theory, J. Reine Angew. Math.473 (1996) 137-179. Zbl0846.31005MR1390686
  12. [12] Hayouni M., Sur la minimisation de la première valeur propre du laplacien, C. R. Acad. Sci. Paris, Sér. I330 (7) (2000) 551-556. Zbl0960.49028MR1760437
  13. [13] Wagner A., Optimal shape problems for eigenvalues, Comm. Partial Differential Equations30 (7–9) (2005). Zbl1121.35038MR2180294
  14. [14] Weiss G.S., Partial regularity for weak solutions of an elliptic free boundary problem, Comm. Partial Differential Equations23 (1998) 439-457. Zbl0897.35017MR1620644
  15. [15] Weiss G.S., Partial regularity for a minimum problem with free boundary, J. Geom. Anal.9 (2) (1999) 317-326. Zbl0960.49026MR1759450

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