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| Description
| - Studies on Earth’s gravity field enable to learn more about our planer. The motivation considered here comes primarily from geodetic applications. We particularly focus on the related mathematics and mathematical tools that form the basis for this research. Historical milestones and famous figures of science in this field are briefly recalled equally as the notion of potential and its first definition. The theory of boundary value problems for elliptic partial differential equations of second order, in particular for Laplace’s and Poisson’s equation, offer a natural basis for gravity field studies, especially in case they rest on terrestrial measurements. Various kinds of free, fixed and mixed boundary value problems are considered. Concerning the linear problems, the classical as well as the weak solution concept is applied. Free boundary value problems are non-linear and are discussed separately. The complex structure of the Earth’s surface makes the solution of the boundary problems rather demanding. Some techniques, that may solve these difficulties, are shown. Also an attempt is made to construct the respective Green’s functions, reproducing kernels and entries in Galerkin’s matrix for the solution domain given by the exterior of an oblate ellipsoid of revolution. The integral kernels are expressed by series of ellipsoidal harmonics and their summation is discussed. Possibilities of using the concept of boundary-value problems for studies that rest on terrestrial gravity measurements in combination with satellite data on gravitational field are considered too. An optimization approach is applied together with the methods above, as the problems to be solved are overdetermined by nature. Finally some questions and stimuli are discussed that are related to physical and mathematical models of the problems mentioned in this contribution.
- Studies on Earth’s gravity field enable to learn more about our planer. The motivation considered here comes primarily from geodetic applications. We particularly focus on the related mathematics and mathematical tools that form the basis for this research. Historical milestones and famous figures of science in this field are briefly recalled equally as the notion of potential and its first definition. The theory of boundary value problems for elliptic partial differential equations of second order, in particular for Laplace’s and Poisson’s equation, offer a natural basis for gravity field studies, especially in case they rest on terrestrial measurements. Various kinds of free, fixed and mixed boundary value problems are considered. Concerning the linear problems, the classical as well as the weak solution concept is applied. Free boundary value problems are non-linear and are discussed separately. The complex structure of the Earth’s surface makes the solution of the boundary problems rather demanding. Some techniques, that may solve these difficulties, are shown. Also an attempt is made to construct the respective Green’s functions, reproducing kernels and entries in Galerkin’s matrix for the solution domain given by the exterior of an oblate ellipsoid of revolution. The integral kernels are expressed by series of ellipsoidal harmonics and their summation is discussed. Possibilities of using the concept of boundary-value problems for studies that rest on terrestrial gravity measurements in combination with satellite data on gravitational field are considered too. An optimization approach is applied together with the methods above, as the problems to be solved are overdetermined by nature. Finally some questions and stimuli are discussed that are related to physical and mathematical models of the problems mentioned in this contribution. (en)
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| Title
| - Boundary problems of mathematical physics in Earth’s gravity field studies
- Boundary problems of mathematical physics in Earth’s gravity field studies (en)
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| skos:prefLabel
| - Boundary problems of mathematical physics in Earth’s gravity field studies
- Boundary problems of mathematical physics in Earth’s gravity field studies (en)
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| skos:notation
| - RIV/00025615:_____/13:#0001901!RIV14-MSM-00025615
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| http://linked.open...avai/predkladatel
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| http://linked.open...avai/riv/aktivita
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| http://linked.open...avai/riv/aktivity
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| http://linked.open...vai/riv/dodaniDat
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| http://linked.open...aciTvurceVysledku
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| http://linked.open.../riv/druhVysledku
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| http://linked.open...iv/duvernostUdaju
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| http://linked.open...titaPredkladatele
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| http://linked.open...dnocenehoVysledku
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| http://linked.open...ai/riv/idVysledku
| - RIV/00025615:_____/13:#0001901
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| http://linked.open...riv/jazykVysledku
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| http://linked.open.../riv/klicovaSlova
| - gravity field studies; boundary value problems in physical geodesy; classical and weak solution concept; Green's function; reproducing kernel; Galerkin's linear system; boundary value problems and combinations of terrestrial and satellite data (en)
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| http://linked.open.../riv/klicoveSlovo
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| http://linked.open...i/riv/kodPristupu
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| http://linked.open...ontrolniKodProRIV
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| http://linked.open...i/riv/mistoVydani
| |
| http://linked.open...telVyzkumneZpravy
| - Leibniz-Societät der Wissenschaften zu Berlin e.V.
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| http://linked.open...in/vavai/riv/obor
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| http://linked.open...ichTvurcuVysledku
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| http://linked.open...cetTvurcuVysledku
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| http://linked.open...vavai/riv/projekt
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| http://linked.open...UplatneniVysledku
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| http://linked.open...iv/tvurceVysledku
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