The index of isolated critical points and solutions of elliptic equations in the plane

G. Alessandrini; R. Magnanini

Annali della Scuola Normale Superiore di Pisa - Classe di Scienze (1992)

  • Volume: 19, Issue: 4, page 567-589
  • ISSN: 0391-173X

How to cite

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Alessandrini, G., and Magnanini, R.. "The index of isolated critical points and solutions of elliptic equations in the plane." Annali della Scuola Normale Superiore di Pisa - Classe di Scienze 19.4 (1992): 567-589. <http://eudml.org/doc/84137>.

@article{Alessandrini1992,
author = {Alessandrini, G., Magnanini, R.},
journal = {Annali della Scuola Normale Superiore di Pisa - Classe di Scienze},
keywords = {index calculus; Gauss-Bonnet theorem; number and character of critical points; gradient length and the curvatures of the level curves},
language = {eng},
number = {4},
pages = {567-589},
publisher = {Scuola normale superiore},
title = {The index of isolated critical points and solutions of elliptic equations in the plane},
url = {http://eudml.org/doc/84137},
volume = {19},
year = {1992},
}

TY - JOUR
AU - Alessandrini, G.
AU - Magnanini, R.
TI - The index of isolated critical points and solutions of elliptic equations in the plane
JO - Annali della Scuola Normale Superiore di Pisa - Classe di Scienze
PY - 1992
PB - Scuola normale superiore
VL - 19
IS - 4
SP - 567
EP - 589
LA - eng
KW - index calculus; Gauss-Bonnet theorem; number and character of critical points; gradient length and the curvatures of the level curves
UR - http://eudml.org/doc/84137
ER -

References

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  1. [A1] G. Alessandrini, Critical points of solutions of elliptic equations in two variables, Ann. Scuola Norm. Sup. Pisa Cl. Sci. (4), 14 (1987), 229-256. Zbl0649.35026MR939628
  2. [A2] G. Alessandrini, Isoperimetric inequalities for the length of level lines of solutions of quasilinear capacity problems in the plane, Z. Angew. Math. Phys.40 (1989), 920-924. Zbl0712.35034MR1027585
  3. [B] L. Bers, Function-theoretical properties of solutions of partial differential equations of elliptic type, Ann. of Math. Stud.33 (1954), 69-94. Zbl0057.08602MR70009
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  9. [Ms] M. Morse, Relations between the critical points of a real function of n independent variables, Trans. Amer. Math. Soc.27, 3 (1925), 345-396. Zbl51.0451.01MR1501318JFM51.0451.01
  10. [P] C. Pucci, An angle's maximum principle for the gradient of solutions of elliptic equations, Boll. Un. Mat. Ital.A (7), 1 (1987), 135-139. Zbl0628.35034MR880110
  11. [PM] K.F. Pagani-Masciadri, Remarks on the critical points of solutions to some quasilinear elliptic equations of second order in the plane, to appear J. Math. Anal. Appl. Zbl0808.35029MR1215631
  12. [R] E.H. Rothe, A relation between the type numbers of a critical point and the index of the corresponding field of gradient vectors, Math. Nachr.4 (1950-51), 12-27. Zbl0044.31903MR40597
  13. [Sa] S. Sakaguchi, Critical points of solutions to the obstacle problem in the plane, preprint. 
  14. [Sch] F. Schulz, Regularity Theory for Quasilinear Elliptic Systems and Monge-Ampère Equations in Two Dimensions, Springer Verlag, New York, 1990. Zbl0709.35038MR1079936
  15. [T] G. Talenti, On functions, whose lines of steepest descent bend proportionally to level lines, Ann. Scuola Norm. Sup. Pisa Cl. Sci. (4), 10 (1983), 587-605. Zbl0542.35007MR753157
  16. [V] I.N. Vekua, Generalized Analytic Functions, Pergamon Press, Oxford, 1962. Zbl0100.07603MR150320
  17. [Wa] J.L. Walsh, The Location of Critical Points of Analytic and Harmonic Functions, American Mathematical Society, New York, 1950. Zbl0041.04101MR37350
  18. [We] C.E. Weatherburn, Differential Geometry of Three Dimensions, Cambridge University Press, Cambridge, 1931. JFM56.0589.01

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