Rellich selection theorem

Let $D$ be an open subset of $\\mathbb{R}^{n}$ . If, for a sequence of functions $f_{i}\\colon D\\to\\mathbb{R}$ , $i=1,2,\\ldots$ there exists a constant $B>0$ such that

(\\forall i)\\qquad\\|f_{i}\\|_{L^{2}(D)}=\\int_{D}f_{i}^{2}\\,d^{n}x<B

and

(\\forall i)\\,(\\forall j\\in\\{1,\\ldots n\\})\\qquad\\int_{D}\\left({\\partial f_{i}%\\over\\partial x_{j}}\\right)^{2}\\,d^{n}x<B

then there exists a subsequence which is convergent in the $L^{2}(D)$ norm.

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