Justification of the limiting absorption principle in R2
A.G.Ramm
TL;DR
This paper justifies the limiting absorption principle for second-order elliptic operators in two-dimensional space, providing necessary and sufficient conditions for its validity based on the right-hand side.
Contribution
It establishes the conditions under which the limiting absorption principle holds for elliptic operators in R2, advancing theoretical understanding.
Findings
Necessary and sufficient conditions identified
Principle validated for specific elliptic operators
Enhanced theoretical framework for R2 analysis
Abstract
The limiting absorption principle in two-dimensional space is justified for a second-order elliptic operators. Necessary and sufficient conditions for the right-hand side are given for this principle to be valid.
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Taxonomy
TopicsNumerical methods in inverse problems · Advanced Mathematical Modeling in Engineering · Advanced Numerical Methods in Computational Mathematics