Heat kernel bounds for higher order elliptic operators

 Access to full text

 Full (PDF)

1. Are Arendt W : Gaussian estimates and interpolation of the spectrum in Lp. Preprint 1993. 
2. Aro Aronson D G : Non-negative solutions of linear parabolic equations. Ann. Sci. Norm. Sup. Pisa (3) 22 (1968) 607-694. Zbl0182.13802MR55 #8553
3. AMT Auscher P, McIntosh A, Tchamitchian P : Noyau de la chaleur d'operateurs elliptiques complexes. Math. Research Lett. 1 (1994) 35-45. Zbl0827.35033MR94k:35081
4. Au Auscher P : Private communication. 
5. BD Barbatis G, Davies E B : Sharp bounds on heat kernels of higher order uniformly elliptic operators. Preprint 1995. Zbl0869.35048
6. BR Bauer L, Reiss E L : Block five diagonal matrices and the fast numerical solution of the biharmonic equation. Math. of Comput. 26 (1972) 311-326. Zbl0257.65034MR47 #1307
7. BS Birman M S, Solomjak M Z : On estimates of singular numbers of integral operators III. Operators on unbounded domains. Vestnik Leningrad State Univ. Math. 2 (1975) 9-27. 
8. C Coffman C V : On the structure of solutions to Δ2u = λu which satisfy the clamped plate conditions on a right angle. SIAM J. Math. Anal. 13 (1982) 746-757. Zbl0498.73010MR84a:35015
9. CD Coffman C V, Duffin R J : On the fundamental eigenvalues of a clamped punctured disk. Adv. Appl. Math. 13 (1992) 142-151. Zbl0762.35073MR93c:35113
10. D1 Davies, E B : Explicit constants for Gaussian upper bounds on heat kernels. Amer J. Math. 109 (1987) 319-334. Zbl0659.35009MR88g:58174
11. D2 Davies E B : Heat Kernels and Spectral Theory. Cambridge University Press, 1989. Zbl0699.35006MR90e:35123
12. D3 Davies E B : The functional calculus. Preprint, 1993. J. London Math. Soc. to appear. Zbl0858.47012
13. D4 Davies E B : Lp spectral independence and L1 analyticity. J. London Math. Soc. to appear. Zbl0913.47032
14. D5 Davies E B : Uniformly elliptic operators with measurable coefficients. J Functional Anal. to appear. Zbl0839.35034
15. D6 Davies E B : Long time asymptotics of fourth order parabolic equations. Preprint 1994. Zbl0851.35018
16. DM Davies E B, Mandouvalos N : heat kernel bounds on hyperbolic space and Kleinian groups. Proc. London Math. Soc. (3) 57 (1988) 182-208. Zbl0643.30035MR89i:58137
17. DST Davies E B, Simon B, Taylor M : Lp spectral theory of Kleinian groups. J. Functional Anal. 78 (1988) 116-136. Zbl0644.58022MR89m:58205
18. ER Elst A F M ter, Robinson D W : Subcoercive and subelliptic operators on Lie groups : Variable coefficients. Publ. RIMS 29 (1993) 745-801. Zbl0816.43002MR95e:22023
19. HS Helffer B and Sjöstrand J : Equation de Schrödinger avec champ magnétique et équation de Harper. pp. 118-197 in «Schrödinger Operators», eds. H Holden and A Jensen, Lecture Notes in Physics, Vol. 345, Springer-Verlag, 1989. Zbl0699.35189
20. HV Hempel R and Voigt J : The spectrum of a Schrödinger operator in Lp(RN) is p-independent. Commun. Math. Phys. 104 (1986) 243-250. Zbl0593.35033MR87h:35247
21. Hö Hörmander L : On the singularities of solutions of partial differential equations, in Proc. Inter. Conf. Tokyo 1969. Univ. of Tokyo Press, Tokyo, 1970, pp 31-40. Zbl0191.10901
22. JN1 Jensen A, Nakamura S : Lp-mapping properties of functions of Schrödinger operators and their applications to scattering theory. J. Math. Soc. Japan 47 (1995) 253-273. Zbl0841.35096MR95m:47087
23. JN2 Jensen A, Nakamura S : Mapping properties of functions of Schrödinger operators between Lp spaces and Besov spaces. pp 187-209 in «Spectral and Scattering Theory and Applications», Advanced Studies in Pure Math. vol. 23, Kinokuniya Publ., Tokyo, 1994. Zbl0815.47012MR96a:47084
24. K Kordyukov Yu A : Lp-theory of elliptic differential operators on manifolds of bounded geometry. Acta Applic. Math. 23 (1991) 223-260. Zbl0743.58030
25. KKM Kozlov V A, Kondrat'ev V A, Maz'ya V G : On sign variation and the absence of «strong» zeros of solutions of elliptic equations. Math. USSR Izvestiya 34 (1990) 337-353. Zbl0701.35062MR90i:35021
26. MNP Maz'ya V G, Nazarov S A, Plamenevskii B A : Absence of the De-Giorgi-type theorems for strongly elliptic operators with complex coefficients. J. Math. Soviet 28 (1985) 726-739. Zbl0562.35030
27. O E.M. Ouhabaz : Gaussian estimates and holomorphy of semigroups. Proc. Amer. Math. Soc. 123 (1995) 1465-1474. Zbl0829.47032MR95f:47068
28. P Pang M M H : Resolvent estimates for Schrödinger operators in Lp(RN) and the theory of exponentially bounded C-semigroups. Semigroups Forum 41 (1990) 97-114. Zbl0739.47017MR91m:35170
29. PV1 Pipher J, Verchota G : A maximum principle for biharmonic functions in Lipschitz and C1 domains. Comment. Math. Helv. 68 (1993) 385-414. Zbl0794.31005MR94j:35030
30. PV2 Pipher J, Verchota G : Dilation invariant estimates and the boundary Gårding inequality for higher order elliptic operators. Ann. Math. to appear. Zbl0878.35035
31. R Robinson D W : Elliptic Operators and Lie Groups. Oxford University Press, 1991. Zbl0747.47030
32. Se Semenov Yu A : Stability of Lp spectrum, in preparation, 1995. 
33. Si1 Simon B : Trace ideals and their applications. London Math. Soc. Lecture Note Series, Vol. 35. Cambridge University Press, 1979. Zbl0423.47001MR80k:47048
34. Si2 Simon B : Schrödinger semigroups. Bull. Amer. Math. Soc. 7 (1982) 447-526. Zbl0524.35002MR86b:81001a
35. St Sturm K-Th : On the Lp-spectrum of Laplace-Beltrami operators. Preprint 1992. 
36. SV Schreieck G, Voigt J : Stability of the Lp spectrum of Schrödinger operators with form small negative part of the potential. In «Functional Analysis», Lecture Notes in Pure and Applied Math. ; Bierstedt, Pietsch, Ruess, Voigt eds. ; Dekker, 1994. Zbl0817.35065
37. VSC Varopoulos N Th, Saloff-Coste L, Coulhon T : Analysis and geometry on groups. Cambridge Tracts in Math., Vol. 100. Cambridge University Press, 1992. Zbl0813.22003MR95f:43008
38. VG Vasil'ev D G, Gol'denveizer A L : Distribution of free vibration frequencies in two- and three-dimensional elastic bodies. p 227-242 of «Mechanics of Deformable Solids», ed. N Kh Arutiunian, I F Obraztsov, V Z Parton. Hemisphere Publ. Co., New York, 1991.