Necessary and Sufficient Condition of Existence for the Quadrature Surfaces Free Boundary Problem
Keywords:
Dirichlet problem, Quadrature surfaces, shape derivative, shape optimization
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.
Published
2020-02-12
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
Section
Chapters
