Optimal conditions for anti-maximum principles
Annali della Scuola Normale Superiore di Pisa - Classe di Scienze, Serie 4, Volume 30 (2001) no. 3-4, p. 499-513
@article{ASNSP_2001_4_30_3-4_499_0,
     author = {Grunau, Hans-Christoph and Sweers, Guido},
     title = {Optimal conditions for anti-maximum principles},
     journal = {Annali della Scuola Normale Superiore di Pisa - Classe di Scienze},
     publisher = {Scuola normale superiore},
     volume = {Ser. 4, 30},
     number = {3-4},
     year = {2001},
     pages = {499-513},
     zbl = {1072.35066},
     mrnumber = {1896075},
     language = {en},
     url = {http://www.numdam.org/item/ASNSP_2001_4_30_3-4_499_0}
}
Grunau, Hans-Christoph; Sweers, Guido. Optimal conditions for anti-maximum principles. Annali della Scuola Normale Superiore di Pisa - Classe di Scienze, Serie 4, Volume 30 (2001) no. 3-4, pp. 499-513. http://www.numdam.org/item/ASNSP_2001_4_30_3-4_499_0/

[1] R.A. Adams, "Sobolev Spaces", Academic Press, New York etc., 1975. | MR 450957 | Zbl 0314.46030

[2] I. Birindelli, Hopf's lemma and anti-maximum principle in general domains, J. Differ. Equations 119 (1995), 450-472. | MR 1340547 | Zbl 0831.35114

[3] T. Boggio, Sullefunzioni di Green d'ordine m, Rend. Circ. Mat. Palermo 20 (1905), 97-135. | JFM 36.0827.01

[4] Ph. Clément - L.A. Peletier, An anti-maximum principle for second order elliptic operators, J. Differ. Equations 34 (1979), 218-229. | MR 550042 | Zbl 0387.35025

[5] Ph. Clément - G. Sweers, Uniform anti-maximum principles, J. Differential Equations 164 (2000), 118-154. | MR 1761420 | Zbl 0964.35033

[6] Ph. Clément - G. Sweers, Uniform anti-maximum principles for polyharmonic operators, Proc. Amer. Math. Soc. 129 (2001), 467-474. | MR 1800235 | Zbl 0959.35044

[7] F. Gazzola - H.-CH. GRUNAU, Critical dimensions and higher order Sobolev inequalities with remainder terms, NODEA 8 (2001), 35-44. | MR 1828947 | Zbl 0990.46021

[8] H.-Ch. Grunau - G. Sweers, Positivity for equations involving polyharmonic operators with Dirichlet boundary conditions, Math. Ann. 307 (1997), 589-626. | MR 1464133 | Zbl 0892.35031

[9] H.-Ch. Grunau - G. Sweers, Positivity for perturbations of polyharmonic operators with Dirichlet boundary conditions in two dimensions, Math. Nachr.179 (1996), 89-102. | MR 1389451 | Zbl 0863.35016

[10] H.-Ch. Grunau - G. Sweers, The maximum principle and positive principal eigenfunctions for polyharmonic equations, In: G. Caristi, E. Mitidieri (eds.), "Reaction Diffusion Systems", Marcel Dekker Inc., New York, Lecture Notes in Pure and Appl. Math. 194 (1998), 163-182. | MR 1472518 | Zbl 0988.35039

[11] H.-Ch. Grunau - G. Sweers, Positivity properties of elliptic boundary value problems of higher order, Proc. 2nd World Congress of Nonlinear Analysts, Nonlinear Analysis, T.M.A. 30 (1997), 5251-5258. | MR 1726027 | Zbl 0894.35016

[12] H.-Ch. Grunau - G. Sweers, Sharp estimates for iterated Greenfunctions, to appear in: Proc. Roy. Soc. Edinburgh Sect. A. | MR 1884473 | Zbl 1115.35009 | Zbl 01735607

[13] P. Jentzsch, Über Integralgleichungen mit positivem Kern, J. Reine Angew. Math. 141 (1912), 235-244. | JFM 43.0429.01

[14] M.A. Krasnosel'Skij - Je. A. Lifshits - A.V. Sobolev, "Positive Linear Systems- The Method of Positive Operators", Heldermann Verlag, Berlin, 1989. | MR 1038527 | Zbl 0674.47036

[15] J.L. Lions - E. Magenes, "Non-homogeneous Boundary Value Problems and Applications I", Springer, Berlin, 1972. | Zbl 0223.35039

[16] Y. Pinchover, Maximum and anti-maximum principles and eigenfunctions estimates via perturbation theory of positive solutions of elliptic equations, Math. Ann. 314 (1999), 555-590. | MR 1704549 | Zbl 0928.35010

[17] Y. Pinchover, On the maximum and anti-maximum principles, Differential equations and mathematical physics (Birmingham, AL, 1999), 323-338, AMS/IP Stud. Adv. Math., 16, Amer. Math. Soc., Providence,RI, 2000. | MR 1764761 | Zbl 1161.35326 | Zbl 01780473

[18] G. Sweers, LN is sharp for the antimaximum principle, J. Differential Equations 134 (1997), 148-153. | MR 1429095 | Zbl 0885.35016

[19] P Takáč, An abstract form of maximum and anti-maximum principles of Hopf's type, J. Math. Anal. Appl. 201 (1996), 339-364. | MR 1396904 | Zbl 0855.35016