Open AccessThe Neumann problem for the equation Δ𝑢-𝑘²𝑢=0 in the exterior of non-closed Lipschitz surfaces
Author(s) -
П. А. Крутицкий
Publication year - 2013
Publication title -
quarterly of applied mathematics
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.603
H-Index - 41
eISSN - 1552-4485
pISSN - 0033-569X
DOI - 10.1090/s0033-569x-2013-01319-4
Subject(s) - algorithm , uniqueness , annotation , computer science , mathematics , artificial intelligence , mathematical analysis
We study the Neumann problem for the equation Δ u − k 2 u = 0 \Delta u - k^2u=0 in the exterior of non-closed Lipschitz surfaces in R 3 R^3 . Theorems on existence and uniqueness of a weak solution of the problem are proved. The integral representation for a solution is obtained in the form of a double layer potential. The density in the potential is defined as a solution of the operator (integral) equation, which is uniquely solvable.