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.
@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},
     pages = {499--513},
     publisher = {Scuola normale superiore},
     volume = {Ser. 4, 30},
     number = {3-4},
     year = {2001},
     zbl = {1072.35066},
     mrnumber = {1896075},
     language = {en},
     url = {http://archive.numdam.org/item/ASNSP_2001_4_30_3-4_499_0/}
}
TY  - JOUR
AU  - Grunau, Hans-Christoph
AU  - Sweers, Guido
TI  - Optimal conditions for anti-maximum principles
JO  - Annali della Scuola Normale Superiore di Pisa - Classe di Scienze
PY  - 2001
DA  - 2001///
SP  - 499
EP  - 513
VL  - Ser. 4, 30
IS  - 3-4
PB  - Scuola normale superiore
UR  - http://archive.numdam.org/item/ASNSP_2001_4_30_3-4_499_0/
UR  - https://zbmath.org/?q=an%3A1072.35066
UR  - https://www.ams.org/mathscinet-getitem?mr=1896075
LA  - en
ID  - ASNSP_2001_4_30_3-4_499_0
ER  - 
%0 Journal Article
%A Grunau, Hans-Christoph
%A Sweers, Guido
%T Optimal conditions for anti-maximum principles
%J Annali della Scuola Normale Superiore di Pisa - Classe di Scienze
%D 2001
%P 499-513
%V Ser. 4, 30
%N 3-4
%I Scuola normale superiore
%G en
%F 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://archive.numdam.org/item/ASNSP_2001_4_30_3-4_499_0/

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

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

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

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

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

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

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

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

[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 | Zbl

[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 | Zbl

[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 | Zbl

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

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

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

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

[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 | Zbl

[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 | Zbl

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

[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 | Zbl