Heat kernel bounds for higher order elliptic operators
Journées équations aux dérivées partielles (1995), article no. 3, 11 p.
     author = {Davies, E. Brian},
     title = {Heat kernel bounds for higher order elliptic operators},
     journal = {Journ\'ees \'equations aux d\'eriv\'ees partielles},
     eid = {3},
     publisher = {Ecole polytechnique},
     year = {1995},
     zbl = {0994.58011},
     mrnumber = {96i:35020},
     language = {en},
     url = {http://archive.numdam.org/item/JEDP_1995____A3_0/}
AU  - Davies, E. Brian
TI  - Heat kernel bounds for higher order elliptic operators
JO  - Journées équations aux dérivées partielles
PY  - 1995
DA  - 1995///
PB  - Ecole polytechnique
UR  - http://archive.numdam.org/item/JEDP_1995____A3_0/
UR  - https://zbmath.org/?q=an%3A0994.58011
UR  - https://www.ams.org/mathscinet-getitem?mr=96i:35020
LA  - en
ID  - JEDP_1995____A3_0
ER  - 
%0 Journal Article
%A Davies, E. Brian
%T Heat kernel bounds for higher order elliptic operators
%J Journées équations aux dérivées partielles
%D 1995
%I Ecole polytechnique
%G en
%F JEDP_1995____A3_0
Davies, E. Brian. Heat kernel bounds for higher order elliptic operators. Journées équations aux dérivées partielles (1995), article  no. 3, 11 p. http://archive.numdam.org/item/JEDP_1995____A3_0/

Are Arendt W : Gaussian estimates and interpolation of the spectrum in Lp. Preprint 1993.

Aro Aronson D G : Non-negative solutions of linear parabolic equations. Ann. Sci. Norm. Sup. Pisa (3) 22 (1968) 607-694. | Numdam | MR | Zbl

AMT Auscher P, Mcintosh A, Tchamitchian P : Noyau de la chaleur d'operateurs elliptiques complexes. Math. Research Lett. 1 (1994) 35-45. | MR | Zbl

Au Auscher P : Private communication.

BD Barbatis G, Davies E B : Sharp bounds on heat kernels of higher order uniformly elliptic operators. Preprint 1995. | Zbl

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. | MR | Zbl

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.

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. | MR | Zbl

CD Coffman C V, Duffin R J : On the fundamental eigenvalues of a clamped punctured disk. Adv. Appl. Math. 13 (1992) 142-151. | MR | Zbl

D1 Davies, E B : Explicit constants for Gaussian upper bounds on heat kernels. Amer J. Math. 109 (1987) 319-334. | MR | Zbl

D2 Davies E B : Heat Kernels and Spectral Theory. Cambridge University Press, 1989. | MR | Zbl

D3 Davies E B : The functional calculus. Preprint, 1993. J. London Math. Soc. to appear. | Zbl

D4 Davies E B : Lp spectral independence and L1 analyticity. J. London Math. Soc. to appear. | Zbl

D5 Davies E B : Uniformly elliptic operators with measurable coefficients. J Functional Anal. to appear. | Zbl

D6 Davies E B : Long time asymptotics of fourth order parabolic equations. Preprint 1994. | Zbl

DM Davies E B, Mandouvalos N : heat kernel bounds on hyperbolic space and Kleinian groups. Proc. London Math. Soc. (3) 57 (1988) 182-208. | MR | Zbl

DST Davies E B, Simon B, Taylor M : Lp spectral theory of Kleinian groups. J. Functional Anal. 78 (1988) 116-136. | MR | Zbl

ER Elst A F M Ter, Robinson D W : Subcoercive and subelliptic operators on Lie groups : Variable coefficients. Publ. RIMS 29 (1993) 745-801. | MR | Zbl

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. | Zbl

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. | MR | Zbl

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. | Zbl

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. | MR | Zbl

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. | MR | Zbl

K Kordyukov Yu A : Lp-theory of elliptic differential operators on manifolds of bounded geometry. Acta Applic. Math. 23 (1991) 223-260. | Zbl

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. | MR | Zbl

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. | Zbl

O E.M. Ouhabaz : Gaussian estimates and holomorphy of semigroups. Proc. Amer. Math. Soc. 123 (1995) 1465-1474. | MR | Zbl

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. | MR | Zbl

PV1 Pipher J, Verchota G : A maximum principle for biharmonic functions in Lipschitz and C1 domains. Comment. Math. Helv. 68 (1993) 385-414. | MR | Zbl

PV2 Pipher J, Verchota G : Dilation invariant estimates and the boundary Gårding inequality for higher order elliptic operators. Ann. Math. to appear. | Zbl

R Robinson D W : Elliptic Operators and Lie Groups. Oxford University Press, 1991. | Zbl

Se Semenov Yu A : Stability of Lp spectrum, in preparation, 1995.

Si1 Simon B : Trace ideals and their applications. London Math. Soc. Lecture Note Series, Vol. 35. Cambridge University Press, 1979. | MR | Zbl

Si2 Simon B : Schrödinger semigroups. Bull. Amer. Math. Soc. 7 (1982) 447-526. | MR | Zbl

St Sturm K-Th : On the Lp-spectrum of Laplace-Beltrami operators. Preprint 1992.

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. | Zbl

VSC Varopoulos N Th, Saloff-Coste L, Coulhon T : Analysis and geometry on groups. Cambridge Tracts in Math., Vol. 100. Cambridge University Press, 1992. | MR | Zbl

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.