Abstract
The heat content of a Borel measurable set \(D \subset \mathbb {R}^N\) at time t is defined by M. van der Berg in [69] (see also [70]) as:
with (T(t))t≥0 being the heat semigroup in \(L^2(\mathbb {R}^N)\). Therefore, the heat content represents the amount of heat in D at time t if in D the initial temperature is 1 and in \(\mathbb {R}^N \setminus D\) the initial temperature is 0.
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Mazón, J.M., Rossi, J.D., Toledo, J.J. (2019). Nonlocal Heat Content. In: Nonlocal Perimeter, Curvature and Minimal Surfaces for Measurable Sets. Frontiers in Mathematics. Birkhäuser, Cham. https://doi.org/10.1007/978-3-030-06243-9_6
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DOI: https://doi.org/10.1007/978-3-030-06243-9_6
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