Abstract and Applied Analysis

Abstract and Applied Analysis / 2004 / Article

Open Access

Volume 2004 |Article ID 579019 | https://doi.org/10.1155/S1085337504306196

Dagmar Medková, "Which solutions of the third problem for the Poisson equation are bounded?", Abstract and Applied Analysis, vol. 2004, Article ID 579019, 10 pages, 2004. https://doi.org/10.1155/S1085337504306196

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

Received10 Sep 2002

Abstract

This paper deals with the problem Δu=g on G and u/n+uf=L on G. Here, Gm, 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 gL2(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.

Copyright © 2004 Hindawi Publishing Corporation. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.


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