Thesis

### On the geometric and analytic properties of some random fractals

Abstract:

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...

### Authors

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Institution:
University of Oxford
Division:
MPLS
Department:
Mathematical Institute
Oxford college:
Lincoln College
Role:
Author

#### Contributors

Division:
MPLS
Department:
Mathematical Institute
Role:
Supervisor
Publication date:
2014
Type of award:
DPhil
Level of award:
Doctoral
Awarding institution:
University of Oxford
Language:
English
Keywords:
Subjects:
UUID:
uuid:a9bbee2c-9958-464a-ac9e-bb8c42e107ea
Local pid:
ora:12474
Deposit date:
2016-05-24