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| Description
| - The aim is to discuss the solution of Neumann's problem interpreted in its oblique derivative version, as it appears in physical geodesy. The problem is formulated in terms of variational methods and the weak solution concept. The motivation comes from the progress of satellite geodesy methods in studies on Earth gravity filed. A possibility is investigated to interpret the solution as a minimization of a quadratic functional, which in the case of the oblique derivative problem leads to an iteration process. The solution is expressed in terms of function bases. In this connection the existence and construction of the reproducing kernel is discussed. Galerkin's system is constructed for the oblique derivative case, which in geodesy corresponds to the gravimetric boundary-value problem. Subsequently, the matrix of this system is simplified slightly, which is compensated by means of successive approximations. Their convergence is discussed. The last section offers some final remarks and an outlook.
- The aim is to discuss the solution of Neumann's problem interpreted in its oblique derivative version, as it appears in physical geodesy. The problem is formulated in terms of variational methods and the weak solution concept. The motivation comes from the progress of satellite geodesy methods in studies on Earth gravity filed. A possibility is investigated to interpret the solution as a minimization of a quadratic functional, which in the case of the oblique derivative problem leads to an iteration process. The solution is expressed in terms of function bases. In this connection the existence and construction of the reproducing kernel is discussed. Galerkin's system is constructed for the oblique derivative case, which in geodesy corresponds to the gravimetric boundary-value problem. Subsequently, the matrix of this system is simplified slightly, which is compensated by means of successive approximations. Their convergence is discussed. The last section offers some final remarks and an outlook. (en)
- Cílem je diskutovat řešení Neumannova problému interpretovaného v jeho verzi se šikmou derivaci. Problém je formulován ve smyslu variačních metod a konceptu slabého řešení. Motivace má své zdroje v pokroku družicových metod studia tíhového pole Země. Vyšetřována je možnost interpretovat řešení jako minimalizaci kvadratického funkcionálu, což v případě šikmé derivace vede k iteračnímu procesu. Řešení je vyjádřeno ve smyslu funkcionálních basí. V této souvislosti je diskutována existence a konstrukce reprodukčního jádra. Galerkinův systém je konstruován pro případ se šikmou derivací, což v geodézii odpovídá gravimetrické okrajové úloze. Následně je pak matice systému mírně zjednodušena a to je kompenzováno pomocí postupných aproximací. Jejich konvergence je diskutována. Poslední odstavec nabízí závěrečné poznámky a výhled. (cs)
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| Title
| - Neumann's boundary-value problem in studies on Earth gravity field: Weak solution
- Neumann's boundary-value problem in studies on Earth gravity field: Weak solution (en)
- Neumannovův okrajový problém při studiu tíhového pole Země: slabé řešení (cs)
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| skos:prefLabel
| - Neumann's boundary-value problem in studies on Earth gravity field: Weak solution
- Neumann's boundary-value problem in studies on Earth gravity field: Weak solution (en)
- Neumannovův okrajový problém při studiu tíhového pole Země: slabé řešení (cs)
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| skos:notation
| - RIV/00025615:_____/05:000013PH!RIV08-GA0-00025615
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| http://linked.open.../vavai/riv/strany
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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:_____/05:000013PH
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| http://linked.open...riv/jazykVysledku
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| http://linked.open.../riv/klicovaSlova
| - Earth's gravity field, geodetic boundary-value problems, Green's functions, varational methods, reproducing kernels, ellipsoidal harmonics, functional analytic estimates (en)
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| http://linked.open.../riv/klicoveSlovo
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| http://linked.open...ontrolniKodProRIV
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| http://linked.open...v/mistoKonaniAkce
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| http://linked.open...i/riv/mistoVydani
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| http://linked.open...i/riv/nazevZdroje
| - 50 years of the Research Institute of Geodesy, Topography and Cartiography, Jubilee Proceedings, Proceedings of VUGTK Research Works, Vol. 50, No. 36
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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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| http://linked.open...vavai/riv/typAkce
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| http://linked.open.../riv/zahajeniAkce
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| number of pages
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| http://purl.org/ne...btex#hasPublisher
| - Resaerch Institute of Geodesy, Topographya and Cartography
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| https://schema.org/isbn
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| is http://linked.open...avai/riv/vysledek
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