Fine singularity analysis of solutions to the Laplace equation: Berg’s effect. (English) Zbl 1344.35012
In the paper Berg’s effect is studied on special domains. This effect is understood as a monotonicity of a harmonic function (with respect to the distance from the center of a flat part of the boundary) restricted to the boundary. The harmonic function must satisfy piecewise constant Neumann boundary conditions. The authors show that Berg’s effect is a rare and fragile phenomenon.
Reviewer: Alla Boikova (Penza)
MSC:
| 35J05 | Laplace operator, Helmholtz equation (reduced wave equation), Poisson equation |
| 35A20 | Analyticity in context of PDEs |
| 31C05 | Harmonic, subharmonic, superharmonic functions on other spaces |
Keywords:
singularities of harmonic functions; polygonal domains; piecewise constant Neumann data; Berg’s effectReferences:
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