Heat Kernel Estimates for Operators with Boundary Conditions
Research Report 97-19
Date: 16 April 1997
We prove Gaussian upper bounds for kernels associated with
non-symmetric, non-autonomous second order parabolic operators of
divergence form subject to various boundary conditions. The growth of
the kernel in time t is determined by the boundary conditions and
geometric properties of the domain. The theory gives a unified
treatment for Dirichlet, Neumann and Robin boundary conditions, and
the existence of a Gaussian type bound is essentially reduced to
verifying some properties of the Hilbert space in the weak formulation
of the problem.
heat kernels. Gaussian estimates. non-autonomous parabolic operators.
boundary value problems.
AMS Subject Classification (1991)
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Sydney Mathematics and Statistics