Optimal conditions for anti-maximum principles
Hans-Christoph Grunau; Guido Sweers
Annali della Scuola Normale Superiore di Pisa - Classe di Scienze (2001)
- Volume: 30, Issue: 3-4, page 499-513
- ISSN: 0391-173X
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topGrunau, Hans-Christoph, and Sweers, Guido. "Optimal conditions for anti-maximum principles." Annali della Scuola Normale Superiore di Pisa - Classe di Scienze 30.3-4 (2001): 499-513. <http://eudml.org/doc/84450>.
@article{Grunau2001,
author = {Grunau, Hans-Christoph, Sweers, Guido},
journal = {Annali della Scuola Normale Superiore di Pisa - Classe di Scienze},
language = {eng},
number = {3-4},
pages = {499-513},
publisher = {Scuola normale superiore},
title = {Optimal conditions for anti-maximum principles},
url = {http://eudml.org/doc/84450},
volume = {30},
year = {2001},
}
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
PB - Scuola normale superiore
VL - 30
IS - 3-4
SP - 499
EP - 513
LA - eng
UR - http://eudml.org/doc/84450
ER -
References
top- [1] R.A. Adams, "Sobolev Spaces", Academic Press, New York etc., 1975. Zbl0314.46030MR450957
- [2] I. Birindelli, Hopf's lemma and anti-maximum principle in general domains, J. Differ. Equations119 (1995), 450-472. Zbl0831.35114MR1340547
- [3] T. Boggio, Sullefunzioni di Green d'ordine m, Rend. Circ. Mat. Palermo20 (1905), 97-135. JFM36.0827.01
- [4] PH. Clément - L.A. Peletier, An anti-maximum principle for second order elliptic operators, J. Differ. Equations34 (1979), 218-229. Zbl0387.35025MR550042
- [5] PH. Clément - G. Sweers, Uniform anti-maximum principles, J. Differential Equations164 (2000), 118-154. Zbl0964.35033MR1761420
- [6] PH. Clément - G. Sweers, Uniform anti-maximum principles for polyharmonic operators, Proc. Amer. Math. Soc.129 (2001), 467-474. Zbl0959.35044MR1800235
- [7] F. Gazzola - H.-CH. GRUNAU, Critical dimensions and higher order Sobolev inequalities with remainder terms, NODEA8 (2001), 35-44. Zbl0990.46021MR1828947
- [8] H.-Ch. Grunau - G. Sweers, Positivity for equations involving polyharmonic operators with Dirichlet boundary conditions, Math. Ann.307 (1997), 589-626. Zbl0892.35031MR1464133
- [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. Zbl0863.35016MR1389451
- [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. Zbl0988.35039MR1472518
- [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. Zbl0894.35016MR1726027
- [12] H.-Ch. Grunau - G. Sweers, Sharp estimates for iterated Greenfunctions, to appear in: Proc. Roy. Soc. Edinburgh Sect. A. Zbl1115.35009MR1884473
- [13] P. Jentzsch, Über Integralgleichungen mit positivem Kern, J. Reine Angew.Math.141 (1912), 235-244. JFM43.0429.01
- [14] M.A. Krasnosel'skij - Je. A. Lifshits - A.V. Sobolev, "Positive Linear Systems- The Method of Positive Operators", Heldermann Verlag, Berlin, 1989. Zbl0674.47036MR1038527
- [15] J.L. Lions - E. Magenes, "Non-homogeneous Boundary Value Problems and Applications I", Springer, Berlin, 1972. Zbl0223.35039
- [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. Zbl0928.35010MR1704549
- [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. Zbl1161.35326MR1764761
- [18] G. Sweers, LN is sharp for the antimaximum principle, J. Differential Equations134 (1997), 148-153. Zbl0885.35016MR1429095
- [19] P Takáč, An abstract form of maximum and anti-maximum principles of Hopf's type, J. Math. Anal. Appl.201 (1996), 339-364. Zbl0855.35016MR1396904
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