Gaussian bounds for the Dirichlet heat kernel

Davies, 1987, Explicit constants for gaussian upper bounds on heat kernels, Amer. J. Math., 109, 319, 10.2307/2374577 Davies, 1987, Heat kernel bounds on manifolds with cusps, J. Funct. Anal., 75, 311, 10.1016/0022-1236(87)90098-X Davies, 1988, Gaussian upper bounds for the heat kernels of some second order operators on riemannian manifolds, J. Funct. Anal., 80, 16, 10.1016/0022-1236(88)90062-6 Davies, 1989, Sharp heat kernel bounds for some Laplace operators, Quart. J. Math. Oxford (2), 40, 281, 10.1093/qmath/40.3.281 Gross, 1976, Logarithmic Sobolev inequalities, Amer. J. Math., 97, 1061, 10.2307/2373688 Lieb, 1967, Calculation of exchange second virial coefficient of a hard sphere gas by path integrals, J. Math. Phys., 8, 43, 10.1063/1.1705099 Molchanov, 1975, Diffusion processes and riemannian geometry, Russian Math. Surveys, 30, 1, 10.1070/RM1975v030n01ABEH001400 Kac, 1951, On some connections between probability theory and differential and integral equations, 189 Ciesielski, 1966, Heat conduction and the principle of not feeling the boundary, Bull. Acad. Polon. Sci. Sér. sci. math., astr. et phys., 14, 435 Varadhan, 1967, Diffusion processes in a small time interval, Comm. Pure Appl. Math., 20, 659, 10.1002/cpa.3160200404 Buslaev, 1968, Continuum integrals and the asymptotic behaviour of the solutions of parabolic equations as t → 0, Vol. 2, 67 Ikeda, 1984, On the asymptotic behaviour of the fundamental solution of the heat equation on certain manifolds, 169 Ikeda, 1988, Short time asymptotics for fundamental solutions of diffusion equations, Springer Lecture Notes in Mathematics, 1322, 37, 10.1007/BFb0077865 Hsu, 1989, Short time asymptotics of the heat kernel on concave boundary, Siam J. Math. Anal., 20, 1109, 10.1137/0520074 Davies, 1987, The equivalence of certain heat kernel and Green function bounds, J. Funct. Anal., 71, 88, 10.1016/0022-1236(87)90017-6 Gradshteyn, 1980 Simon, 1978, Classical boundary conditions as a technical tool in modern mathematical physics, Adv. in Math., 30, 377, 10.1016/0001-8708(78)90040-3 Whittaker, 1927