no. 6
The Optimal Shape of a Dendrite Sealed at Both Ends
Annales de l'I.H.P. Analyse non linéaire, Tome 26 (2009) no. 6, pp. 2317-2333 
@article{AIHPC_2009__26_6_2317_0,
     author = {Privat, Yannick},
     title = {The {Optimal} {Shape} of a {Dendrite} {Sealed} at {Both} {Ends}},
     journal = {Annales de l'I.H.P. Analyse non lin\'eaire},
     pages = {2317--2333},
     year = {2009},
     publisher = {Elsevier},
     volume = {26},
     number = {6},
     doi = {10.1016/j.anihpc.2009.04.004},
     mrnumber = {2569896},
     language = {en},
     url = {https://www.numdam.org/articles/10.1016/j.anihpc.2009.04.004/}
}
TY  - JOUR
AU  - Privat, Yannick
TI  - The Optimal Shape of a Dendrite Sealed at Both Ends
JO  - Annales de l'I.H.P. Analyse non linéaire
PY  - 2009
SP  - 2317
EP  - 2333
VL  - 26
IS  - 6
PB  - Elsevier
UR  - https://www.numdam.org/articles/10.1016/j.anihpc.2009.04.004/
DO  - 10.1016/j.anihpc.2009.04.004
LA  - en
ID  - AIHPC_2009__26_6_2317_0
ER  - 
%0 Journal Article
%A Privat, Yannick
%T The Optimal Shape of a Dendrite Sealed at Both Ends
%J Annales de l'I.H.P. Analyse non linéaire
%D 2009
%P 2317-2333
%V 26
%N 6
%I Elsevier
%U https://www.numdam.org/articles/10.1016/j.anihpc.2009.04.004/
%R 10.1016/j.anihpc.2009.04.004
%G en
%F AIHPC_2009__26_6_2317_0
Privat, Yannick. The Optimal Shape of a Dendrite Sealed at Both Ends. Annales de l'I.H.P. Analyse non linéaire, Tome 26 (2009) no. 6, pp. 2317-2333. doi: 10.1016/j.anihpc.2009.04.004

[1] Bandle C., Extremal Problems for Eigenvalues of the Sturm-Liouville Type, in: General Inequalities, 5, Oberwolfach, 1986, Internat. Schriftenreibe Numer. Math., vol. 80, Birkhäuser, Basel, 1987. | Zbl | MR

[2] Cox S. J., Lipton R., Extremal Eigenvalue Problems for Two-Phase Conductors, Arch. Ration. Mech. Anal. 136 (1996) 101-117. | Zbl | MR

[3] Cox S. J., Raol J. H., Recovering the Passive Properties of Tapered Dendrites From Single and Dual Potential Recordings, Math. Biosci. 190 (1) (2004) 9-37. | Zbl | MR

[4] Dautray R., Lions J. L., Analyse Mathématique Et Calcul Numérique Pour Les Sciences Et Les Techniques, Masson, 1988. | Zbl

[5] Egorov Y., Kondratiev V., On Spectral Theory of Elliptic Operators, Birkhäuser, 1996. | Zbl | MR

[6] Gilbarg D., Trudinger N. S., Elliptic Partial Differential Equations of Second Order, Springer-Verlag, New York, Heidelberg, 1977, 327-340. | Zbl | MR

[7] Henrot A., Extremum Problems for Eigenvalues of Elliptic Operators, Front. Math., Birkhäuser, 2006. | Zbl | MR

[8] Henrot A., Privat Y., Shape Minimisation of Dendritic Attenuation, Appl. Math. Optim. 57 (1) (February 2008) 1-16. | Zbl | MR

[9] Henrot A., Pierre M., Variation Et Optimisation De Formes, Math. Appl., Springer-Verlag, 2005. | MR

[10] Tosio Kato X., Perturbation Theory for Linear Operators, Classics Math., Springer-Verlag, Berlin, 1995, reprint of the 1980 edition. | Zbl | MR

[11] Mauroy B., Filoche M., Weibel E. R., Sapoval B., An Optimal Bronchial Tree May Be Dangerous, Nature 427 (2004) 633-636.

[12] Mauroy B., Filoche M., Andrade J. S., Sapoval B., Interplay Between Geometry and Flow Distribution in an Airway Tree, Phys. Rev. Lett. 90 (2003) 148101-1-148101-4.

[13] Rall W., An Historical Perspective on Modeling Dendrites, in: Stuart G., Spruston N., Häusser M. (Eds.), Dendrites, 2nd edition, Oxford University Press, 2008, Chapter 12.

[14] Rall W., Agmon-Snir H., Cable Theory for Dendritic Neurons, in: Koch C., Segev I. (Eds.), Methods in Neuronal Modeling. From Ions to Networks, 2nd edition, MIT Press, Cambridge, MA, 1998, pp. 27-92, Chapter 2.

[15] Rall W., Theory of Physiological Properties of Dendrites, Ann. New York Acad. Sci. 96 (1962) 1071.

[16] Sokolowski J., Zolesio J. P., Introduction to Shape Optimization: Shape Sensitivity Analysis, Springer Ser. Comput. Math., vol. 10, Springer, Berlin, 1992. | Zbl | MR

[17] Walter J., Regular Eigenvalue Problem With Eigenvalue Parameter in the Boundary Condition, Math. Z. 133 (1973) 301-312. | Zbl | MR

Cité par Sources :