Infinite boundary value problems for surfaces of constant mean curvature

1972 ◽  
Vol 49 (1) ◽  
pp. 1-31 ◽  
Author(s):  
Joel Spruck
Keyword(s):  
Boundary Value Problems ◽  
Mean Curvature ◽  
Constant Mean Curvature ◽  
Boundary Value

Boundary tracing and boundary value problems: II. Applications

2007 ◽  
Vol 463 (2084) ◽  
pp. 1925-1938 ◽  
Author(s):  
Michael L Anderson ◽  
Andrew P Bassom ◽  
Neville Fowkes
Keyword(s):  
Partial Differential Equations ◽  
Exact Solutions ◽  
Boundary Value Problems ◽  
Mean Curvature ◽  
Constant Mean Curvature ◽  
Boundary Value ◽  
Practical Significance ◽  
Curvature Equation ◽  
Mean Curvature Equation ◽  
Boundary Tracing

This is the second of a pair of papers describing the use of boundary tracing for boundary value problems. In the preceding article, the theory of the technique was explained and it was shown how it enables one to use known exact solutions of partial differential equations to generate new solutions. Here, we illustrate the use of the technique by applying it to three equations of practical significance: Helmholtz's equation, Poisson's equation and the nonlinear constant mean curvature equation. A variety of new solutions are obtained and the potential of the technique for further application outlined.

SYMMETRY RESULT FOR SOME OVERDETERMINED VALUE PROBLEMS

2008 ◽  
Vol 49 (4) ◽  
pp. 479-494 ◽  
Author(s):  
MOHAMMED BARKATOU ◽  
SAMIRA KHATMI
Keyword(s):  
Maximum Principle ◽  
Boundary Value Problems ◽  
Neumann Problem ◽  
Compatibility Condition ◽  
Mean Curvature ◽  
Boundary Value ◽  
The Maximum Principle ◽  
The Mean ◽  
The Neumann Problem ◽  
Symmetry Result

AbstractThe aim of this article is to prove a symmetry result for several overdetermined boundary value problems. For the two first problems, our method combines the maximum principle with the monotonicity of the mean curvature. For the others, we use essentially the compatibility condition of the Neumann problem.

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