Interfaces of Prescribed Mean Curvature

  • I. Tamanini


Several questions of mathematical and physical interest lead to the consideration of an “energy functional” of the following type:
$$F[V] = \text{(weighted area of}\, S) + \int_{v}\, H dv,$$
where S is the surface bounding the region V of n-space and H is a given summable function. In the following, we shall be concerned with a problem of this type, representing in a sense a simplified physical situation, and investigate some basic properties of its solutions. The results we obtain may serve both as an illustration of the use of certain variational techniques and as an instance of results that could be obtained, under appropriate conditions, in more general cases.


Minimal Surface Model Problem Negative Part Obstacle Problem Soap Bubble 
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© Springer-Verlag New York Inc. 1987

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  • I. Tamanini

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