Abstract
This paper studies precise estimates of integral kernels of some integral operators on the boundary of bounded and strictly convex domains with sufficiently regular boundary. Assume that an integral operator on has the integral kernel with estimate (, ). Then, from the Neumann series, the operator is also an integral operator. The problem is whether the integral kernel of can be estimated by the term up to a constant or not. If the boundary is strictly convex, such types of estimates hold.
The most important point is that the obtained estimates have the same decaying behavior as and the same exponential term as for the original kernel . These advantages are essentially needed to handle some inverse initial boundary value problems whose governing equation is the heat equation in three dimensions.
Citation
Masaru Ikehata. Mishio Kawashita. "Estimates of the integral kernels arising from inverse problems for a three-dimensional heat equation in thermal imaging." Kyoto J. Math. 54 (1) 1 - 50, Spring 2014. https://doi.org/10.1215/21562261-2400265
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