On the geometric and analytic properties of some random fractals
The heat content of a domain D of ℝd is defined as
E(s) = ∫D u(s,x)dx,
where u is the solution to the heat equation with zero initial condition and unit Dirichlet boundary condition. This thesis studies the behaviour of E(s) for small s with a particular emphasis on the case where $D$ is a planar domain whose boundary is a random Koch curve.
When ∂D is spatially homogeneous, we show th...Expand abstract
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- Philippe H. A. Charmoy
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