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?
This paper deals with the problem on and on . Here, , , is a bounded domain with Lyapunov boundary, is a bounded nonnegative function on the boundary of , is a bounded linear functional on representable by a real measure on the boundary of , and , . It is shown that a weak solution of this problem is bounded in if and only if the Newtonian potential corresponding to the boundary condition is bounded in .
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