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Izv. Akad. Nauk SSSR Ser. Mat., 1989, Volume 53, Issue 2, Pages 328–344 (Mi izv1243)  

This article is cited in 18 scientific papers (total in 19 papers)

On sign variation and the absence of “strong” zeros of solutions of elliptic equations

V. A. Kozlov, V. A. Kondrat'ev, V. G. Maz'ya


Abstract: The authors prove the existence of a convex domain $G$ with smooth boundary for which an eigenfunction corresponding to an eigenvalue of problem with operators of elliptic type is of variable sign.
Bibliography: 10 titles.

Full text: PDF file (1475 kB)
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English version:
Mathematics of the USSR-Izvestiya, 1990, 34:2, 337–353

Bibliographic databases:

UDC: 517.9
MSC: Primary 35J40; Secondary 35P99
Received: 08.07.1987

Citation: V. A. Kozlov, V. A. Kondrat'ev, V. G. Maz'ya, “On sign variation and the absence of “strong” zeros of solutions of elliptic equations”, Izv. Akad. Nauk SSSR Ser. Mat., 53:2 (1989), 328–344; Math. USSR-Izv., 34:2 (1990), 337–353

Citation in format AMSBIB
\Bibitem{KozKonMaz89}
\by V.~A.~Kozlov, V.~A.~Kondrat'ev, V.~G.~Maz'ya
\paper On sign variation and the absence of ``strong'' zeros of solutions of elliptic equations
\jour Izv. Akad. Nauk SSSR Ser. Mat.
\yr 1989
\vol 53
\issue 2
\pages 328--344
\mathnet{http://mi.mathnet.ru/izv1243}
\mathscinet{http://www.ams.org/mathscinet-getitem?mr=998299}
\zmath{https://zbmath.org/?q=an:0701.35062}
\transl
\jour Math. USSR-Izv.
\yr 1990
\vol 34
\issue 2
\pages 337--353
\crossref{https://doi.org/10.1070/IM1990v034n02ABEH000649}


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    Citing articles on Google Scholar: Russian citations, English citations
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    This publication is cited in the following articles:
    1. Charles V Coffman, Richard J Duffin, “On the fundamental eigenfunctions of a clamped punctured disk”, Advances in Applied Mathematics, 13:2 (1992), 142  crossref
    2. Hans-Christoph Grunau, “Positive solutions to semilinear polyharmonic Dirichlet problems involving critical Sobolev exponents”, Calc Var, 3:2 (1995), 243  crossref  mathscinet  zmath
    3. Hans — Christoph Grunau, Guido Sweers, “Positivity for Perturbations of Polyharmonic Operators with Dirichlet Boundary Conditions in Two Dimensions”, Math Nachr, 179:1 (1996), 89  crossref  mathscinet  zmath  isi
    4. Grunau Hans-Christoph, Guido Sweers, “Positivity properties of elliptic boundary value problems of higher order”, Nonlinear Analysis: Theory, Methods & Applications, 30:8 (1997), 5251  crossref
    5. M.P. Owen, “Asymptotic First Eigenvalue Estimates for the Biharmonic Operator on a Rectangle”, Journal of Differential Equations, 136:1 (1997), 166  crossref
    6. B Brown, “An efficient direct solver for a class of mixed finite element problems”, Applied Numerical Mathematics, 38:1-2 (2001), 1  crossref  elib
    7. Milan D. Mihajlović, David J. Silvester, “Efficient parallel solvers for the biharmonic equation”, Parallel Computing, 30:1 (2004), 35  crossref
    8. A.B. Andreev, R.D. Lazarov, M.R. Racheva, “Postprocessing and higher order convergence of the mixed finite element approximations of biharmonic eigenvalue problems”, Journal of Computational and Applied Mathematics, 182:2 (2005), 333  crossref
    9. S. A. Nazarov, G. H. Sweers, “Boundary value problems for the bi-harmonic equation and for the iterated Laplacian in a three-dimensional domain with an edge”, J. Math. Sci. (N. Y.), 143:2 (2007), 2936–2960  mathnet  crossref  mathscinet  zmath  elib
    10. Axel Osses, Jean-Pierre Puel, “Unique continuation property near a corner and its fluid-structure controllability consequences”, ESAIM COCV, 15:2 (2009), 279  crossref  isi
    11. Hans-Christoph Grunau, “Nonlinear Questions in Clamped Plate Models”, Milan j math, 2009  crossref  isi
    12. Marcos Montenegro, “On nontrivial solutions of critical polyharmonic elliptic systems”, Journal of Differential Equations, 247:3 (2009), 906  crossref
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    14. Pedro R S Antunes, “On the buckling eigenvalue problem”, J. Phys. A: Math. Theor, 44:21 (2011), 215205  crossref
    15. M. S. Agranovich, I. V. Astashova, L. A. Bagirov, V. V. Vlasov, V. V. Zhikov, Yu. S. Ilyashenko, V. V. Kozlov, A. A. Kon'kov, S. I. Pokhozhaev, E. V. Radkevich, N. Kh. Rozov, I. N. Sergeev, A. L. Skubachevskii, G. A. Chechkin, A. S. Shamaev, T. A. Shaposhnikova, “Vladimir Alexandrovich Kondratiev. July 2, 1935 – March 11, 2010”, Journal of Mathematical Sciences, 190:1 (2013), 1–7  mathnet  crossref  mathscinet
    16. M. D. Surnachev, “Asymptotic behavior of positive solutions to Emden–Fowler type equations”, J Math Sci, 2011  crossref
    17. Hans-Christoph Grunau, Guido Sweers, “In any dimension a “clamped plate” with a uniform weight may change sign”, Nonlinear Analysis: Theory, Methods & Applications, 97 (2014), 119  crossref
    18. Hans-Christoph Grunau, Guido Sweers, “A clamped plate with a uniform weight may change sign”, DCDS-S, 7:4 (2014), 761  crossref
    19. Mohammed Al-Gwaiz, Vieri Benci, Filippo Gazzola, “Bending and stretching energies in a rectangular plate modeling suspension bridges”, Nonlinear Analysis: Theory, Methods & Applications, 106 (2014), 18  crossref
  • Известия Академии наук СССР. Серия математическая Izvestiya: Mathematics
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