Heat Kernel Estimates for Operators with Boundary Conditions


Daniel Daners


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.

Key phrases

heat kernels. Gaussian estimates. non-autonomous parabolic operators. boundary value problems.

AMS Subject Classification (1991)

Primary: 35K20


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