@article{ASNSP_1992_4_19_4_567_0, author = {Alessandrini, Giovanni 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}, zbl = {0793.35021}, mrnumber = {1205884}, language = {en}, url = {www.numdam.org/item/ASNSP_1992_4_19_4_567_0/} }
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, Série 4, Tome 19 (1992) no. 4, pp. 567-589. http://www.numdam.org/item/ASNSP_1992_4_19_4_567_0/
[A1] Critical points of solutions of elliptic equations in two variables, Ann. Scuola Norm. Sup. Pisa Cl. Sci. (4), 14 (1987), 229-256. | Numdam | MR 939628 | Zbl 0649.35026
,[A2] 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 1027585 | Zbl 0712.35034
,[B] Function-theoretical properties of solutions of partial differential equations of elliptic type, Ann. of Math. Stud. 33 (1954), 69-94. | MR 70009 | Zbl 0057.08602
,[D] Theory of Hp Spaces, Academic Press, New York, 1970. | MR 268655 | Zbl 0215.20203
,[F] Geometric Measure Theory, Springer Verlag, New York, 1969. | MR 257325 | Zbl 0176.00801
,[K-S] An Introduction to Variational Inequalities and Their Applications, Academic Press, New York, 1980. | MR 567696 | Zbl 0457.35001
- ,[Mi] Differential Topology, Princeton University Press, Princeton, 1958.
,[Mo] Multiple Integrals in the Calculus of Variations, Springer Verlag, New York, 1966. | MR 202511 | Zbl 0142.38701
,[Ms] Relations between the critical points of a real function of n independent variables, Trans. Amer. Math. Soc. 27, 3 (1925), 345-396. | JFM 51.0451.01 | MR 1501318
,[P] An angle's maximum principle for the gradient of solutions of elliptic equations, Boll. Un. Mat. Ital. A (7), 1 (1987), 135-139. | MR 880110 | Zbl 0628.35034
,[PM] 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 1215631 | Zbl 0808.35029
,[R] 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 40597 | Zbl 0044.31903
,[Sa] Critical points of solutions to the obstacle problem in the plane, preprint.
,[Sch] Regularity Theory for Quasilinear Elliptic Systems and Monge-Ampère Equations in Two Dimensions, Springer Verlag, New York, 1990. | MR 1079936 | Zbl 0709.35038
,[T] 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 753157 | Zbl 0542.35007
,[V] Generalized Analytic Functions, Pergamon Press, Oxford, 1962. | MR 150320 | Zbl 0100.07603
,[Wa] The Location of Critical Points of Analytic and Harmonic Functions, American Mathematical Society, New York, 1950. | MR 37350 | Zbl 0041.04101
,[We] Differential Geometry of Three Dimensions, Cambridge University Press, Cambridge, 1931. | JFM 56.0589.01
,