Necessary and Sufficient Condition of Existence for the Quadrature Surfaces Free Boundary Problem
Theory and Applications of Mathematical Science Vol. 2,
Page 71-80
Abstract
Combining the shape derivative [1] to the maximum principle, we show that the so-called Quadrature Surfaces Free Boundary Problem has a solution which contains strictly the support of if and only if
where and is the convex hull of the support of
We also give a necessary and sufficient condition of existence for the problem where the term source is a uniform density supported by a segment.
Keywords:
- Dirichlet problem
- Quadrature surfaces
- shape derivative
- shape optimization
How to Cite
Barkatou, M. (2020). Necessary and Sufficient Condition of Existence for the Quadrature Surfaces Free Boundary Problem. Theory and Applications of Mathematical Science Vol. 2, 71-80. Retrieved from https://stm1.bookpi.org/index.php/tams-v2/article/view/1023
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