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Which solutions of the third problem for the Poisson equation are bounded?

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  • Dagmar Medková

Abstract

This paper deals with the problem Δ u = g on G and ∂ u / ∂ n + u f = L on ∂ G . Here, G ⊂ ℝ m , m > 2 , is a bounded domain with Lyapunov boundary, f is a bounded nonnegative function on the boundary of G , L is a bounded linear functional on W 1 , 2 ( G ) representable by a real measure μ on the boundary of G , and g ∈ L 2 ( G ) ∩ L p ( G ) , p > m / 2 . It is shown that a weak solution of this problem is bounded in G if and only if the Newtonian potential corresponding to the boundary condition μ is bounded in G .

Suggested Citation

  • Dagmar Medková, 2004. "Which solutions of the third problem for the Poisson equation are bounded?," Abstract and Applied Analysis, Hindawi, vol. 2004, pages 1-10, January.
    • Handle: RePEc:hin:jnlaaa:579019
    DOI: 10.1155/S1085337504306196
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