Necessary and Sufficient Condition of Existence for the Quadrature Surfaces Free Boundary Problem
نویسنده
چکیده
Performing the shape derivative (Sokolowski and Zolesio, 1992) and using the maximum principle, we show that the so-called Quadrature Surfaces free boundary problem QS ( f , k) ⎪⎪⎪⎨⎪⎪⎪⎩ −ΔuΩ = f in Ω uΩ = 0 on ∂Ω |∇uΩ| = k (constant) on ∂Ω. has a solution which contains strictly the support of f if and only if ∫
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تاریخ انتشار 2010