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Uspekhi Mat. Nauk, 1963, Volume 18, Issue 1(109), Pages 3–62 (Mi umn6301)  

This article is cited in 35 scientific papers (total in 35 papers)

Some problems of the qualitative theory of second order elliptic equations (case of several independent variables)

E. M. Landis


Full text: PDF file (5017 kB)

English version:
Russian Mathematical Surveys, 1963, 18:1, 1–62

Bibliographic databases:

MSC: 35J25, 35B05, 32V15, 47B25, 35A05
Received: 06.07.1962

Citation: E. M. Landis, “Some problems of the qualitative theory of second order elliptic equations (case of several independent variables)”, Uspekhi Mat. Nauk, 18:1(109) (1963), 3–62; Russian Math. Surveys, 18:1 (1963), 1–62

Citation in format AMSBIB
\Bibitem{Lan63}
\by E.~M.~Landis
\paper Some problems of the qualitative theory of second order elliptic equations (case of several independent variables)
\jour Uspekhi Mat. Nauk
\yr 1963
\vol 18
\issue 1(109)
\pages 3--62
\mathnet{http://mi.mathnet.ru/umn6301}
\mathscinet{http://www.ams.org/mathscinet-getitem?mr=150437}
\zmath{https://zbmath.org/?q=an:0125.05802}
\transl
\jour Russian Math. Surveys
\yr 1963
\vol 18
\issue 1
\pages 1--62
\crossref{https://doi.org/10.1070/RM1963v018n01ABEH004124}


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    Erratum
    • Corrections
      Uspekhi Mat. Nauk, 1963, 18:4(112), 241–242


    This publication is cited in the following articles:
    1. I. S. Arshon, “On the decrease of harmonic functions of three variables in a solid of revolution”, Math. USSR-Izv., 2:4 (1968), 725–733  mathnet  crossref  mathscinet  zmath
    2. M. A. Pak, “On the decrease of solutions of linear elliptic equations with constant coefficients”, Math. USSR-Sb., 7:3 (1969), 347–351  mathnet  crossref  mathscinet  zmath
    3. E. G. Sitnikova, “A strong zero theorem for an elliptic equation of high order”, Math. USSR-Sb., 10:3 (1970), 349–367  mathnet  crossref  mathscinet  zmath
    4. E. G. Sitnikova, “A three spheres theorem for an elliptic equation of high order”, Math. USSR-Sb., 11:2 (1970), 189–195  mathnet  crossref  mathscinet  zmath
    5. G. N. Blokhina, “Theorems of Phragmén–Lindelöf type for linear elliptic equations of second order”, Math. USSR-Sb., 11:4 (1970), 467–490  mathnet  crossref  mathscinet  zmath
    6. B. S. Mityagin, G. M. Henkin, “Linear problems of complex analysis”, Russian Math. Surveys, 26:4 (1971), 99–164  mathnet  crossref  mathscinet  zmath
    7. E. M. Landis, O. A. Oleinik, “Generalized analyticity and some related properties of solutions of elliptic and parabolic equations”, Russian Math. Surveys, 29:2 (1974), 195–212  mathnet  crossref  mathscinet  zmath
    8. I. S. Arshon, “Phragmén–Lindelöf theorems for the solutions of an elliptic system in two independent variables with constant coefficients”, Math. USSR-Izv., 8:4 (1974), 909–936  mathnet  crossref  mathscinet  zmath
    9. E. M. Landis, “Ob odnoi teoreme tipa Fragmena–Lindelefa dlya reshenii ellipticheskikh uravnenii”, UMN, 30:5(185) (1975), 213–213  mathnet  mathscinet  zmath
    10. V. M. Miklyukov, “On the asymptotic properties of subsolutions of quasilinear equations of elliptic type and mappings with bounded distortion”, Math. USSR-Sb., 39:1 (1981), 37–60  mathnet  crossref  mathscinet  zmath  isi
    11. V. V. Minakhin, “A pair of Riemannian metrics on a complete manifold”, Funct. Anal. Appl., 14:2 (1980), 138–140  mathnet  crossref  mathscinet  zmath
    12. V. V. Minakhin, “Liouville's theorem and Harnack's inequality for Beltrami's equation on an arbitrary manifold”, Funct. Anal. Appl., 14:2 (1980), 140–142  mathnet  crossref  mathscinet  zmath
    13. V. M. Miklyukov, “On the structure of level sets and the growth of subsolutions of equations of elliptic type”, Russian Math. Surveys, 36:1 (1981), 240–241  mathnet  crossref  mathscinet  zmath  adsnasa  isi
    14. P. A. Kuchment, “Floquet theory for partial differential equations”, Russian Math. Surveys, 37:4 (1982), 1–60  mathnet  crossref  mathscinet  zmath  adsnasa  isi
    15. A. A. Novruzov, “On an approach to the study of qualitative properties of solutions of nondivergence elliptic equations of second order”, Math. USSR-Sb., 50:2 (1985), 343–367  mathnet  crossref  mathscinet  zmath
    16. N. S. Nadirashvili, “Multiple eigenvalues of the Laplace operator”, Math. USSR-Sb., 61:1 (1988), 225–238  mathnet  crossref  mathscinet  zmath
    17. V. A. Kondrat'ev, E. M. Landis, “On qualitative properties of solutions of a nonlinear equation of second order”, Math. USSR-Sb., 63:2 (1989), 337–350  mathnet  crossref  mathscinet  zmath
    18. N. S. Nadirashvili, “On the length of the nodal curve of an eigenfunction of the Laplace operator”, Russian Math. Surveys, 43:4 (1988), 227–228  mathnet  crossref  mathscinet  zmath  adsnasa  isi
    19. S. B. Kuksin, “Perturbation of quasiperiodic solutions of infinite-dimensional Hamiltonian systems”, Math. USSR-Izv., 32:1 (1989), 39–62  mathnet  crossref  mathscinet  zmath
    20. V. A. Kozlov, “The strong zero theorem for an elliptic boundary value problem in an angle”, Math. USSR-Sb., 67:1 (1990), 283–302  mathnet  crossref  mathscinet  zmath  isi
    21. V. A. Kondrat'ev, A. A. Kon'kov, “On properties of solutions of a class of nonlinear second-order equations”, Russian Acad. Sci. Sb. Math., 83:1 (1995), 67–77  mathnet  crossref  mathscinet  zmath  isi
    22. Raymond Brummelhuis, “Three-spheres theorem for second order elliptic equations”, J Anal Math, 65:1 (1995), 179  crossref  mathscinet  zmath  isi
    23. A. A. Kon'kov, “Behavior at infinity of solutions of second-order nonlinear equations of a particular class”, Math. Notes, 60:1 (1996), 22–28  mathnet  crossref  crossref  mathscinet  zmath  isi
    24. Jin Cheng, Masahiro Yamamoto, Inverse Probl, 14:4 (1998), 869  crossref  mathscinet  zmath  isi
    25. A L Bukhgeim, J Cheng, M Yamamoto, Inverse Probl, 15:4 (1999), 1021  crossref  mathscinet  zmath  adsnasa  isi
    26. A. A. Kon'kov, “On non-negative solutions of quasilinear elliptic inequalities”, Izv. Math., 63:2 (1999), 255–329  mathnet  crossref  crossref  mathscinet  zmath  isi  elib
    27. H. Matevossian, S. V. Pikulin, “On the homogenization of semilinear elliptic operators in perforated domains”, Sb. Math., 193:3 (2002), 409–422  mathnet  crossref  crossref  mathscinet  zmath  isi  elib
    28. Nazarov, F, “Sign and area in nodal geometry of Laplace eigenfunctions”, American Journal of Mathematics, 127:4 (2005), 879  crossref  isi
    29. A. A. Kon'kov, “The behaviour of solutions of elliptic inequalities that are non-linear with respect to the highest derivatives”, Izv. Math., 71:1 (2007), 15–51  mathnet  crossref  crossref  mathscinet  zmath  isi  elib  elib
    30. Sergio Vessella, “Quantitative estimates of unique continuation for parabolic equations, determination of unknown time-varying boundaries and optimal stability estimates”, Inverse Probl, 24:2 (2008), 023001  crossref  mathscinet  zmath  isi
    31. Xiangxing Tao, “Quantitative unique continuation for Neumann problems of elliptic equations with weight”, Math Meth Appl Sci, 2009, n/a  crossref
    32. Herbert Koch, Daniel Tataru, “Carleman Estimates and Unique Continuation for Second Order Parabolic Equations with Nonsmooth Coefficients”, Communications in Partial Differential Equations, 34:4 (2009), 305  crossref
    33. Zhang Songyan, “Three-sphere inequalities for second order singular partial differential equations”, Acta Mathematica Scientia, 30:3 (2010), 993  crossref
    34. S. V. Pikulin, “Convergence of a family of solutions to a Fujita-type equation in domains with cavities”, Comput. Math. Math. Phys., 56:11 (2016), 1872–1900  mathnet  crossref  crossref  isi  elib
    35. A. I. Ibragimov, A. I. Nazarov, “On Phragmén — Lindelöf principle for Non-divergence Type Elliptic Equations and Mixed Boundary conditions”, Matematicheskaya fizika i kompyuternoe modelirovanie, 20:3 (2017), 65–76  mathnet  crossref
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