Critical points of solutions of elliptic equations in two variables
Annali della Scuola Normale Superiore di Pisa - Classe di Scienze, Serie 4, Volume 14 (1987) no. 2, pp. 229-256.
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author = {Alessandrini, Giovanni},
title = {Critical points of solutions of elliptic equations in two variables},
journal = {Annali della Scuola Normale Superiore di Pisa - Classe di Scienze},
pages = {229--256},
publisher = {Scuola normale superiore},
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year = {1987},
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Alessandrini, Giovanni. Critical points of solutions of elliptic equations in two variables. Annali della Scuola Normale Superiore di Pisa - Classe di Scienze, Serie 4, Volume 14 (1987) no. 2, pp. 229-256. http://www.numdam.org/item/ASNSP_1987_4_14_2_229_0/

[1] S. Agmon, A. Douglis and L. Nirenberg, Estimates near the boundary for solutions of elliptic partial differential equations satisfying general boundary conditions I, Comm. Pure Appl. Math. 12, 623-727 (1959). | MR | Zbl

[2] G. Alessandrini, An identification problem for an elliptic equation in two variables, Ann. Mat. Pura Appl. (4) 145, 265-296 (1986). | MR | Zbl

[3] S. Bernstein, Sur la généralization du problème de Dirichlet (I), Math. Ann. 62, 253-271 (1906). | JFM | MR

[4] L. Bers and L. Nirenberg, On a representation theorem for linear elliptic systems with discontinuous coefficient.s and its applications, in: Convegno Internazionale sulle Equazioni Lineari alle Derivate Parziali, Trieste, 111-140, Cremonese, Roma, 1955. | MR | Zbl

[5] D. Gilbarg and J. Serrin, On isolated singularities of solutions of second order elliptic differential equations, J. Analyse Math. 4, 309-340 (1956). | MR | Zbl

[6] D. Gilbarg and N.S. Trudinger, Elliptic Partial Differential Equations of Second Order, Springer-Verlag, Berlin, 1983. | MR | Zbl

[7] P. Hartman and A. Wintner, On the local behaviour of solutions of non-parabolic partial differential equations (I), Amer. J. Math. 75, 449-476 (1953). | MR | Zbl

[8] P. Hartman and A. Wintner, On the local behaviour of solutions of non-parabolic partial differential equations (II) The uniqueness of the Green singularity, Amer. J. Math. 76, 351-361 (1954). | MR | Zbl

[9] P. Hartman and A. Wintner, On the local behaviour of solutions of non-parabolic partial differential equations (III) Approximation by spherical harmonics, Amer. J. Math. 77, 329-354 (1955). | MR | Zbl

[10] K. Miller, Barriers on cones for uniformly elliptic operators, Ann. Mat. Pura Appl. (4) 76, 93-105 (1967). | MR | Zbl

[11] L.A. Peletier and J. Serrin, Gradient bounds and Liouville theorems for quasilinear elliptic equations, Ann. Scuola Norm. Sup. Pisa Cl. Sci., (4) 5, 65-104 (1978). | Numdam | MR | Zbl

[12] T. Radó, The problem of the least area and the problem of Plateau, Math. Z. 32, 763-796 (1930). | JFM | MR

[13] J. Serrin, Removable singularities of solutions of elliptic equations, Arc. Rat. Mech. Anal. 17, 67-78 (1964). | MR | Zbl

[14] R.P. Sperb, Maximum Principles and their Applications, Academic Press, New York, 1981. | MR | Zbl

[15] G. Talenti, Equazioni lineari ellittiche in due variabili, Matematiche (Catania) 21, 339-376 (1966). | MR | Zbl

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