Which solutions of the third problem for the Poisson equation are bounded?. (17th May 2004)

• Record Type: Journal Article
• Authors: Medková, Dagmar
• Is Part Of: Abstract and applied analysis. Volume 2004:Number 6(2004)
• Page Start: 501
• Page End: 510
• Publication Date: 2004-05-17
• Subjects: Mathematical analysis -- Periodicals; Mathematical analysis; Applied Mathematics; Mathematical Analysis; Periodicals; 515.05
• DOI: 10.1155/S1085337504306196
• Languages: English
• ISSNs: 1085-3375

Abstract

Abstract : This paper deals with the problemΔ u = g onG 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 ofG, L is a bounded linear functional onW 1, 2 ( G ) representable by a real measureμ on the boundary ofG, andg ∈ L 2 ( G ) ∩ L p ( G ), p > m / 2 . It is shown that a weak solution of this problem is bounded inG if and only if the Newtonian potential corresponding to the boundary conditionμ is bounded inG .