21 citations · 67 across the 20 of their papers we have counts for
5 papers · 1 filter
Qualitative properties of the heat content
Michiel van den Berg, Katie Gittins
We obtain monotonicity and convexity results for the heat content of domains in Riemannian manifolds and in Euclidean space subject to various initial temperature conditions. We in…
Heat flow in polygons with reflecting edges
Sam Farrington, Katie Gittins
We investigate the heat flow in an open, bounded set in with polygonal boundary . We suppose that contains an open, bounded set w…
Heat flow from polygons
Michiel van den Berg, Peter Gilkey, Katie Gittins
We study the heat flow from an open, bounded set in with a polygonal boundary . The initial condition is the indicator function of . A Dirichlet bound…
On the heat content of a polygon
Michiel van den Berg, Katie Gittins
Let be a bounded, connected, open set in Euclidean space with polygonal boundary. Suppose has initial temperature and the complement of has initial…
Uniform bounds for the heat content of open sets in Euclidean space
Michiel van den Berg, Katie Gittins
We obtain (i) lower and upper bounds for the heat content of an open set in with -smooth boundary and finite Lebesgue measure, (ii) a necessary and sufficient geo…