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

How to cite

top

Grunau, 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. [1] R.A. Adams, "Sobolev Spaces", Academic Press, New York etc., 1975. Zbl0314.46030MR450957
  2. [2] I. Birindelli, Hopf's lemma and anti-maximum principle in general domains, J. Differ. Equations119 (1995), 450-472. Zbl0831.35114MR1340547
  3. [3] T. Boggio, Sullefunzioni di Green d'ordine m, Rend. Circ. Mat. Palermo20 (1905), 97-135. JFM36.0827.01
  4. [4] PH. Clément - L.A. Peletier, An anti-maximum principle for second order elliptic operators, J. Differ. Equations34 (1979), 218-229. Zbl0387.35025MR550042
  5. [5] PH. Clément - G. Sweers, Uniform anti-maximum principles, J. Differential Equations164 (2000), 118-154. Zbl0964.35033MR1761420
  6. [6] PH. Clément - G. Sweers, Uniform anti-maximum principles for polyharmonic operators, Proc. Amer. Math. Soc.129 (2001), 467-474. Zbl0959.35044MR1800235
  7. [7] F. Gazzola - H.-CH. GRUNAU, Critical dimensions and higher order Sobolev inequalities with remainder terms, NODEA8 (2001), 35-44. Zbl0990.46021MR1828947
  8. [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. [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. [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. [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. [12] H.-Ch. Grunau - G. Sweers, Sharp estimates for iterated Greenfunctions, to appear in: Proc. Roy. Soc. Edinburgh Sect. A. Zbl1115.35009MR1884473
  13. [13] P. Jentzsch, Über Integralgleichungen mit positivem Kern, J. Reine Angew.Math.141 (1912), 235-244. JFM43.0429.01
  14. [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. [15] J.L. Lions - E. Magenes, "Non-homogeneous Boundary Value Problems and Applications I", Springer, Berlin, 1972. Zbl0223.35039
  16. [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. [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. [18] G. Sweers, LN is sharp for the antimaximum principle, J. Differential Equations134 (1997), 148-153. Zbl0885.35016MR1429095
  19. [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

NotesEmbed ?

top

You must be logged in to post comments.

To embed these notes on your page include the following JavaScript code on your page where you want the notes to appear.

Only the controls for the widget will be shown in your chosen language. Notes will be shown in their authored language.

Tells the widget how many notes to show per page. You can cycle through additional notes using the next and previous controls.

    
                

Note: Best practice suggests putting the JavaScript code just before the closing </body> tag.