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

Dagmar Medková

Abstract and Applied Analysis, 2004, vol. 2004, 1-10

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 .

Date: 2004
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Persistent link: https://EconPapers.repec.org/RePEc:hin:jnlaaa:579019

DOI: 10.1155/S1085337504306196

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