# Rellich selection theorem

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

$$ |

and

$$ |

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

Title | Rellich selection theorem |
---|---|

Canonical name | RellichSelectionTheorem |

Date of creation | 2013-03-22 14:38:55 |

Last modified on | 2013-03-22 14:38:55 |

Owner | rspuzio (6075) |

Last modified by | rspuzio (6075) |

Numerical id | 7 |

Author | rspuzio (6075) |

Entry type | Theorem |

Classification | msc 46C05 |