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Levandovskyy, Viktor; Schönemann, Hans

doi:10.1145/860854.860895

Cited by 35 publications

(1 citation statement)

References 15 publications

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“…However, the above system is extremely symmetric and hence poses hard problems when we try to solve it this way (this was done in collaboration with V. Levandovskyy [9] with a non-commutative version of Singular [7]). …”

Section: Second Order Split Operatorsmentioning

confidence: 99%

Split operators for oblique boundary value problems

Bauer

2008

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In the field of gravity determination a special kind of boundary value problem respectively ill-posed satellite problem occurs; the data and hence side condition of our PDE are oblique second order derivatives of the gravitational potential.In mathematical terms this means that our gravitational potential v fulfills ∆v = 0 in the exterior space of the Earth Σ ext and Dv = f on the discrete data location which is on the Earth's surface Σ for terrestrial measurements and on a satellite track in Σ ext for spaceborne measurement campaigns. D is a first order derivative for methods like geometric astronomic levelling and satellite-to-satellite tracking (e.g. CHAMP); it is a second order derivative for other methods like terrestrial gradiometry and satellite gravity gradiometry (e.g. GOCE).Classically one can handle first order side conditions which are not tangential to the Σ and second derivatives pointing in the radial direction employing integral and pseudo differential equation methods. We will present a different approach: We classify all first and purely second order operators D which fulfill ∆Dv = 0 if ∆v = 0. This allows us to solve the problem with oblique side conditions as if we had ordinary i.e. non-derived side conditions. The only additional work which has to be done is an inversion of D, i.e. integration.

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Section: Second Order Split Operatorsmentioning

confidence: 99%