This is a preview of subscription content, log in via an institution to check access.
References
Berg, M. van den: On the spectrum of the Dirichlet Laplacian for horn-shaped regions in ℝn with infinite volume. J. Funct. Anal.58, 150–156 (1984)
Berg, M. van den: On the asymptotics of the heat equation and bounds on traces associated with the Dirichlet Laplacian. J. Funct. Anal.71, 279–293 (1987)
Berg, M. van den, Srisatkunarajah, S.: Heat flow and brownian motion for a region in ℝ2 with a polygonal boundary. (Preprint 1989)
Berg, M. van den: Gaussian bounds for the Dirichlet heat kernel. J. Funct. Anal. (to appear)
Carslaw, H.S., Jaeger, J.C.: Conduction of heat in solids. Oxford: Clarendon Press 1986
Davies, E.B.: Some norm bounds and quadratic form inequalities for Schrödinger operators, II. J. Oper. Theory12, 177–196 (1984)
Davies, E.B.: Trace properties of the Dirichlet Laplacian. Math. Zeit.188, 245–251 (1985)
Davies, E.B. One-parameter semigroups. New York: Academic Press 1980
Davies, E.B.: Heat kernels and spectral theory. Cambridge: Cambridge University Press 1989
Davies, E.B., Mandouvalos, N.: Heat kernel bounds on manifolds with cusps. J. Funct. Anal.75, 311–322 (1987)
Davies, E.B., Simon, B.: Ultracontractivity and the heat kernel for Schrödinger operators and Dirichlet Laplacians. J. Funct. Anal.59, 335–395 (1984)
Edmunds, D.E., Evans, W.D.: Spectral theory and differential operators. Oxford: Clarendon Press 1987
Fleckinger, J.: Asymptotic distribution of eigenvalues of elliptic operators on unbounded domains. In: Everitt, W.N., Sleeman, B.D. (eds) Ordinary and partial differential equations. Proceedings, Dundee 1980. (Lect. Notes Math., vol. 846, pp. 119–128) Berlin Heidelberg New York: Springer 1981
Gradshteyn, I.S., Ryzhik, I.M.: Table of integrals, series and products, New York: Academic Press 1980
Maz'ja, V.G.: On (p, l)-capacity, imbedding theorems and the spectrum of a selfadjoint elliptic operator. Math. USSR, Izv.7, 357–387 (1973)
Rosen, J.: Sobolev inequalities for weight spaces and supercontractivity. Trans. Am. Math. Soc.222, 367–376 (1976)
Rozenbljum, V.G.: The eigenvalues of the first boundary value problem in unbounded domains. Math. USSR, Sb.18, 235–248 (1972)
Rozenbljum, V.G.: The calculation of the spectral properties for the Laplace operator in domains of infinite measure. In: Smirnov, V.I. (ed.) Problems of mathematical analysis. No. 4: Integral and differential operators. Differential equations. Leningrad: Izdat. Leningrad Univ. 1973
Simon, B.: Functional integration and quantum physics. New York: Academic Press 1979
Simon, B.: Classical boundary, conditions as a technical tool in modern mathematical physics. Adv. Math.30, 377–385 (1978)
Simon, B.: Some quantum operators with discrete spectrum but classically continuous spectrum. Ann. Phys.146, 209–220 (1983)
Simon, B.: Non-classical eigenvalue asymptotics. J. Funct. Anal.53, 84–98 (1983)
Tamura, H.: The asymptotic distribution of eigenvalues of the Laplace operator in an unbounded domain. Nagoya Math. J.60, 7–33 (1976)
Author information
Authors and Affiliations
Rights and permissions
About this article
Cite this article
van den Berg, M., Davies, E.B. Heat flow out of regions in ℝm . Math Z 202, 463–482 (1989). https://doi.org/10.1007/BF01221585
Received:
Accepted:
Issue Date:
DOI: https://doi.org/10.1007/BF01221585