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Double Integral on Closed Disc

Source: IMS 2009

May 20, 2009
calculusintegrationfunctionreal analysisreal analysis unsolved

Problem Statement

Suppose that f:R2ā†’R f: \mathbb R^2\rightarrow \mathbb R is a non-negative and continuous function that \iint_{\mathbb R^2}f(x,y)dxdy\equal{}1. Prove that there is a closed disc D D with the least radius possible such that \iint_D f(x,y)dxdy\equal{}\frac12.
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