The index of isolated critical points and solutions of elliptic equations in the plane
Annali della Scuola Normale Superiore di Pisa - Classe di Scienze, Serie 4, Volume 19 (1992) no. 4, pp. 567-589.
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     author = {Alessandrini, G. and Magnanini, R.},
     title = {The index of isolated critical points and solutions of elliptic equations in the plane},
     journal = {Annali della Scuola Normale Superiore di Pisa - Classe di Scienze},
     pages = {567--589},
     publisher = {Scuola normale superiore},
     volume = {Ser. 4, 19},
     number = {4},
     year = {1992},
     mrnumber = {1205884},
     zbl = {0793.35021},
     language = {en},
     url = {http://www.numdam.org/item/ASNSP_1992_4_19_4_567_0/}
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Alessandrini, G.; 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, Serie 4, Volume 19 (1992) no. 4, pp. 567-589. http://www.numdam.org/item/ASNSP_1992_4_19_4_567_0/

[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. | Numdam | MR | Zbl

[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. | MR | Zbl

[B] L. Bers, Function-theoretical properties of solutions of partial differential equations of elliptic type, Ann. of Math. Stud. 33 (1954), 69-94. | MR | Zbl

[D] P.L. Duren, Theory of Hp Spaces, Academic Press, New York, 1970. | MR | Zbl

[F] F. Federer, Geometric Measure Theory, Springer Verlag, New York, 1969. | MR | Zbl

[K-S] D. Kinderlehrer - G. Stampacchia, An Introduction to Variational Inequalities and Their Applications, Academic Press, New York, 1980. | MR | Zbl

[Mi] J. Milnor, Differential Topology, Princeton University Press, Princeton, 1958.

[Mo] C.B. Morrey, Multiple Integrals in the Calculus of Variations, Springer Verlag, New York, 1966. | MR | Zbl

[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. | JFM | MR

[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. | MR | Zbl

[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. | MR | Zbl

[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. | MR | Zbl

[Sa] S. Sakaguchi, Critical points of solutions to the obstacle problem in the plane, preprint.

[Sch] F. Schulz, Regularity Theory for Quasilinear Elliptic Systems and Monge-Ampère Equations in Two Dimensions, Springer Verlag, New York, 1990. | MR | Zbl

[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. | Numdam | MR | Zbl

[V] I.N. Vekua, Generalized Analytic Functions, Pergamon Press, Oxford, 1962. | MR | Zbl

[Wa] J.L. Walsh, The Location of Critical Points of Analytic and Harmonic Functions, American Mathematical Society, New York, 1950. | MR | Zbl

[We] C.E. Weatherburn, Differential Geometry of Three Dimensions, Cambridge University Press, Cambridge, 1931. | JFM