Critical points of solutions of elliptic equations in two variables

Giovanni Alessandrini

Annali della Scuola Normale Superiore di Pisa - Classe di Scienze (1987)

  • Volume: 14, Issue: 2, page 229-256
  • ISSN: 0391-173X

How to cite

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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 14.2 (1987): 229-256. <http://eudml.org/doc/84005>.

@article{Alessandrini1987,
author = {Alessandrini, Giovanni},
journal = {Annali della Scuola Normale Superiore di Pisa - Classe di Scienze},
keywords = {uniformly elliptic; critical points; Dirichlet data},
language = {eng},
number = {2},
pages = {229-256},
publisher = {Scuola normale superiore},
title = {Critical points of solutions of elliptic equations in two variables},
url = {http://eudml.org/doc/84005},
volume = {14},
year = {1987},
}

TY - JOUR
AU - Alessandrini, Giovanni
TI - Critical points of solutions of elliptic equations in two variables
JO - Annali della Scuola Normale Superiore di Pisa - Classe di Scienze
PY - 1987
PB - Scuola normale superiore
VL - 14
IS - 2
SP - 229
EP - 256
LA - eng
KW - uniformly elliptic; critical points; Dirichlet data
UR - http://eudml.org/doc/84005
ER -

References

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  1. [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). Zbl0093.10401MR125307
  2. [2] G. Alessandrini, An identification problem for an elliptic equation in two variables, Ann. Mat. Pura Appl. (4) 145, 265-296 (1986). Zbl0662.35118MR886713
  3. [3] S. Bernstein, Sur la généralization du problème de Dirichlet (I), Math. Ann.62, 253-271 (1906). Zbl37.0383.01MR1511375JFM37.0383.01
  4. [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. Zbl0067.32503MR76981
  5. [5] D. Gilbarg and J. Serrin, On isolated singularities of solutions of second order elliptic differential equations, J. Analyse Math.4, 309-340 (1956). Zbl0071.09701MR81416
  6. [6] D. Gilbarg and N.S. Trudinger, Elliptic Partial Differential Equations of Second Order, Springer-Verlag, Berlin, 1983. Zbl0562.35001MR737190
  7. [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). Zbl0052.32201MR58082
  8. [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). Zbl0055.32403MR64271
  9. [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). Zbl0066.08001MR76156
  10. [10] K. Miller, Barriers on cones for uniformly elliptic operators, Ann. Mat. Pura Appl. (4) 76, 93-105 (1967). Zbl0149.32101MR221087
  11. [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). Zbl0383.35025MR481493
  12. [12] T. Radó, The problem of the least area and the problem of Plateau, Math. Z.32, 763-796 (1930). Zbl56.0436.01MR1545197JFM56.0436.01
  13. [13] J. Serrin, Removable singularities of solutions of elliptic equations, Arc. Rat. Mech. Anal.17, 67-78 (1964). Zbl0135.15601MR170095
  14. [14] R.P. Sperb, Maximum Principles and their Applications, Academic Press, New York, 1981. Zbl0454.35001MR615561
  15. [15] G. Talenti, Equazioni lineari ellittiche in due variabili, Matematiche (Catania) 21, 339-376 (1966). Zbl0149.07402MR204845
  16. [16] J.L. Walsh, The Location of Critical Points of Analytic and Harmonic Functions, American Mathematical Society, New York, 1950. Zbl0041.04101MR37350

Citations in EuDML Documents

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  1. Shigeru Sakaguchi, Critical points of solutions to the obstacle problem in the plane
  2. G. Alessandrini, R. Magnanini, The index of isolated critical points and solutions of elliptic equations in the plane
  3. B. Helffer, T. Hoffmann-Ostenhof, S. Terracini, Nodal domains and spectral minimal partitions
  4. Mikhail Karpukhin, Gerasim Kokarev, Iosif Polterovich, Multiplicity bounds for Steklov eigenvalues on Riemannian surfaces
  5. Bernard Helffer, Domaines nodaux et partitions spectrales minimales

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