Sharp estimates for iterated Green functions

Royal Society of Edinburgh - Proceedings A

Volumn 132, Issue 1, 2002, Pages 91-120

  Grunau, H Ch ^a   Sweers, G ^b  

^a OTTO VON GUERICKE UNIVERSITY   (Germany)

^b DELFT UNIVERSITY OF TECHNOLOGY   (Netherlands)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 0036993256     PISSN: 03082105     EISSN: None     Source Type: Journal    
DOI: 10.1017/s0308210500001542     Document Type: Conference Paper

References (22)

1. A. Ancona. Comparaison des mesures harmoniques et des fonctions de Green pour des opérateurs elliptiques sur un domaine lipschitzien. C. R. Acad. Sci. Paris Sér. I 294 (1982), 505-508.
2. G. Barbatis and E. B. Davies. Sharp bounds on heat kernels of higher order uniformly elliptic operators. J. Operat. Theory 36 (1996), 179-198.
3. T. Boggio. Sulle funzioni di Green d'ordine m. Rendi. Circ. Mat. Palermo 20 (1905), 97-135.
4. K. L. Chung and Zh. Zhao. From Brownian motion to Schrödinger's equation (Springer, 1995).
5. Ph. Clément and G. Sweers. Uniform anti-maximum principles. J. Diff. Eqns 164 (2000). 118-154.
6. M. Cranston and T. R. McConnell. The lifetime of conditioned Brownian motion. Z. Wahrscheinlichkeitsth. 65 (1983), 1-11.
7. E. B. Davies. Heat kernels and spectral theory (Cambridge University Press, 1989).
8. p-spectral theory of higher-order elliptic differential operators. Bull. Lond. Math. Soc. 29 (1997), 513-546.
9. E. B. Davies. Pointwise lower bounds on the heat kernels of higher order elliptic operators. Math. Proc. Camb. Phil. Soc. 125 (1999), 105-111.
10. H.-Ch. Grunau and G. Sweers. Positivity for perturbations of polyharmonic operators with Dirichlet boundary conditions in two dimensions. Math. Nachr. 179 (1996), 89-102.
11. H.-Ch. Grunau and G. Sweers. Positivity for equations involving polyharmonic operators with Dirichlet boundary conditions. Math. Ann. 307 (1997), 589-626.
12. H.-Ch. Grunau and G. Sweers. The maximum principle and positive principal eigenfunctions for polyharmonic equations. In Reaction diffusion systems (ed. G. Caristi and E. Mitidieri), pp. 163-182, Lecture Notes in Pure and Applied Mathematics, vol. 194 (New York; Marcel Dekker, 1998).
13. H.-Ch. Grunau and G. Sweers. Optimal conditions for anti-maximum principles. Annli Scuola Norm. Sup. Pisa. (In the press.)
14. P. Jentzsch. Über Integralgleichungen mit positivem Kern. J. Reine Angew. Math. 141 (1912), 235-244.
15. Yu. P. Krasovskiǐ. Green function properties and generalized solutions of elliptic boundary value problems (Russian). Izv. Akad. Nauk SSSR Ser. Math. 33 (1969). 109-137. (English transl. Math. USSR Izv. 3 (1969), 105-130.)
16. Yu. P. Krasovskiǐ. Green function properties and generalized solutions of elliptic boundary value problems (Russian). Izv. Akad. Nauk SSSR Ser. Math. 33 (1969). 109-137. (English transl. Math. USSR Izv. 3 (1969), 105-130.)
17. E. Mitidieri and G. Sweers. Weakly coupled elliptic systems and positivity. Math. Nachr. 173 (1995), 259-286.
18. F. Schulz. Regularity theory for quasilinear elliptic systems and Monge-Ampère equations in two dimensions. Lecture Notes in Mathematics, vol. 1445 (Springer, 1990).
19. G. Sweers. Positivity for a strongly coupled elliptic system by Green function estimates. J. Geom. Analysis 4 (1994), 121-142.
20. P. Takáč. An abstract form of maximum and anti-maximum principles of Hopf's type. J. Math. Analysis Applic. 201 (1996), 339-364.
21. K.-O. Widman. Inequalities for the Green function and boundary continuity of the gradient of solutions of elliptic differential equations. Math. Scand. 21 (1967), 17-37.
22. Zh. Zhao. Green function for Schrödinger operator and conditioned Feynman-Kac gauge. J. Math. Analysis Applic. 116 (1986), 309-334.