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

Dagmar Medková

Abstract and Applied Analysis, 2004, vol. 2004, issue 6, 501-510

Abstract: This paper deals with the problem Δu = g on G and ∂u/∂n + uf = L on ∂G. Here, G ⊂ ℝm, 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 W1,2(G) representable by a real measure μ on the boundary of G, and g ∈ L2(G)∩Lp(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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https://doi.org/10.1155/S1085337504306196

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Persistent link: https://EconPapers.repec.org/RePEc:wly:jnlaaa:v:2004:y:2004:i:6:p:501-510

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