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The most interesting multidimensional case is d=2.
The extension to systems and to the multidimensional case is done in a simplified way which does not preserve the scalar order of accuracy.
However, the multidimensional case is rather different, and there is no general understanding of the situation.
Similar(57)
Resonances for the multidimensional case were studied by Melrose, Sjöstrand, and Zworski and other, see [23, 25, 28]) and references therein.
The delicate sonic cases can be easily treated and the extension to multidimensional cases is obtained using the dimensional splitting technique.
EVENT also has a competitive speed for the simpler, less-heterogeneous multidimensional cases but it is slower than SHDOM for more variable cases.
In the sequel of this paper, this approach has been extended to the multidimensional case.
In the setting of point measures we introduce a damped gradient that was lacking in the multidimensional case.
Thus, Theorem 7 can be translated in a multidimensional case as follows.
More importantly, the results including the fast computation algorithm obtained for the LPM in the one-dimensional case can be extended directly to the multidimensional case.
The Sturm-Liouville problems in domains with piecewise smooth boundary are also of great interest in multidimensional case.
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Justyna Jupowicz-Kozak
CEO of Professional Science Editing for Scientists @ prosciediting.com