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  • The solution of the weak Neumann problem for the Laplace equation with a distribution as a boundary condition is studied on a general open set G in the Euclidean space. It is shown that the solution of the problem is the sum of a constant and the Newtonian potential corresponding to a distribution with finite energy supported on the boundary. If we look for a solution of the problem in this form we get a bounded linear operator. Under mild assumptions on G a necessary and sufficient condition for the solvability of the problem is given and the solution is constructed.
  • The solution of the weak Neumann problem for the Laplace equation with a distribution as a boundary condition is studied on a general open set G in the Euclidean space. It is shown that the solution of the problem is the sum of a constant and the Newtonian potential corresponding to a distribution with finite energy supported on the boundary. If we look for a solution of the problem in this form we get a bounded linear operator. Under mild assumptions on G a necessary and sufficient condition for the solvability of the problem is given and the solution is constructed. (en)
  • Na obecné otevřené podmnožině G Euklidova prostoru je studováno slabé řešení Neumannovy úlohy pro Laplaceovu rovnici s distribucí jako hraniční podmínkou. Je dokázáno, že řešení problému je součet konstanty a Newtonova potenciálu odpovídajícímu distribuci s konečnou energií s nosičem na hranici. Jestliže hledáme řešení úlohy v této formě, dostáváme omezený lineární operátor. Při slabých předpokladech na G jsou dány nutné a postačující podmínky pro řešitelnost úlohy a řešení je zkonstruováno. (cs)
Title
  • The Neumann Problem for the Laplace Equation on General Domains
  • The Neumann Problem for the Laplace Equation on General Domains (en)
  • Neumannova úloha pro Laplaceovu rovnici na obecných oblastech (cs)
skos:prefLabel
  • The Neumann Problem for the Laplace Equation on General Domains
  • The Neumann Problem for the Laplace Equation on General Domains (en)
  • Neumannova úloha pro Laplaceovu rovnici na obecných oblastech (cs)
skos:notation
  • RIV/67985840:_____/07:00092526!RIV08-AV0-67985840
http://linked.open.../vavai/riv/strany
  • 1107;1139
http://linked.open...avai/riv/aktivita
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  • Z(AV0Z10190503)
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  • 4
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  • 436978
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  • RIV/67985840:_____/07:00092526
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  • Laplace equation; Neumann problem; potential (en)
http://linked.open.../riv/klicoveSlovo
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  • CZ - Česká republika
http://linked.open...ontrolniKodProRIV
  • [E576A1409584]
http://linked.open...i/riv/nazevZdroje
  • Czechoslovak Mathematical Journal
http://linked.open...in/vavai/riv/obor
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http://linked.open...cetTvurcuVysledku
http://linked.open...UplatneniVysledku
http://linked.open...v/svazekPeriodika
  • 57
http://linked.open...iv/tvurceVysledku
  • Medková, Dagmar
http://linked.open...n/vavai/riv/zamer
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  • 0011-4642
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