scholarly journals The weak Dirichlet and Neumann problem for the Laplacian in Lq for bounded and exterior domains. Applications.

1990 ◽  
pp. 180-223 ◽  
Author(s):  
Christian G. Simader
Keyword(s):  
Neumann Problem ◽  
Exterior Domains

scholarly journals Multiple solutions for some Neumann problems in exterior domains

2006 ◽  
Vol 73 (3) ◽  
pp. 353-364 ◽  
Author(s):  
Tsing-San Hsu ◽  
Huei-Li Lin
Keyword(s):  
Neumann Problem ◽  
Multiple Solutions ◽  
The Other ◽  
Exterior Domains ◽  
Neumann Problems ◽  
The Neumann Problem

In this paper, we show that if q(x) satisfies suitable conditions, then the Neumann problem -Δu+u = q(x)ⅠuⅠp−2u in Ω has at least two solutions of which one is positive and the other changes sign.

8.—Constructive Methods for Solving the Exterior Neumann Problem for the Reduced Wave Equation in a Spherically Symmetric Medium

1976 ◽  
Vol 75 (2) ◽  
pp. 97-107 ◽  
Author(s):  
David Colton ◽  
Wolfgang Wendland
Keyword(s):  
Wave Equation ◽  
Integral Operator ◽  
Neumann Problem ◽  
Acoustic Waves ◽  
Homogeneous Medium ◽  
Radiation Condition ◽  
Spherically Symmetric ◽  
Exterior Domains ◽  
Constructive Methods ◽  
Scattering Of Acoustic Waves

SYNOPSISAn integral operator is constructed which maps solutions of the reduced wave equation defined in exterior domains onto solutions of ∆n u+λ2(l+B(r))u = 0 (*) defined in exterior domains, where B(r) is a continuously differentiable function of compact support. This operator is then used to construct a solution to the exterior Neumann problem for (*) satisfying the Sommerfeld radiation condition at infinity. Such problems arise in connection with the scattering of acoustic waves in a non-homogeneous medium, and this paper gives a method for solving these problems which is suitable for analytic and numerical approximations.

Semilinear Neumann problem in exterior domains

1998 ◽  
Vol 31 (7) ◽  
pp. 791-821 ◽  
Author(s):  
Xing-Bin Pan ◽  
Xuefeng Wang
Keyword(s):  
Neumann Problem ◽  
Exterior Domains

On the critical Neumann problem with weight in exterior domains

2003 ◽  
Vol 54 (1) ◽  
pp. 143-163 ◽  
Author(s):  
J. Chabrowski ◽  
Bernhard Ruf
Keyword(s):  
Neumann Problem ◽  
Exterior Domains

scholarly journals Mixed Biharmonic Dirichlet-Neumann Problem in Exterior Domains

2020 ◽  
pp. 755-762
Author(s):  
Hovik A. Matevossian
Keyword(s):  
Neumann Problem ◽  
Unique Solvability ◽  
Biharmonic Equation ◽  
Compact Set ◽  
Uniqueness Theorems ◽  
Exterior Domains ◽  
Dirichlet Integral

We study the unique solvability of the mixed Dirichlet-Neumann problem for the biharmonic equation in the exterior of a compact set under the assumption that solutions of this problem has a bounded Dirichlet integral with weight |x|a. Depending on the value of the parameter a, we obtained uniqueness (non-uniqueness) theorems of the problem or present exact formulas for the dimension of the space of solutions of the mixed Dirichlet-Neumann problem

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