## Abstract

Given a bounded below, lower semi-continuous function f on an infinite dimensional Banach space or a non-compact manifold X, we consider various possibilities of perturbing f by an element p of a reasonable class of functions A in such a way that for the new functional f-p, the minimization problem inf
_{X} (f-p) is well-posed (i.e., every minimizing sequence is convergent). These perturbed minimization principles are quite powerful and have a wide array of applications in Banach space theory, potential theory, non-smooth analysis, non-linear analysis, the variational approach to differential equations as well as in the theory of viscosity solutions for Hamilton-Jacobi equations.

Original language | English (US) |
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Title of host publication | Handbook of the Geometry of Banach Spaces |

Editors | W B Johnson, J Lindenstrauss |

Publisher | North-Holland, Amsterdam |

Pages | 393-435 |

Number of pages | 43 |

Volume | 1 |

Edition | C |

ISBN (Print) | 9780444828422 |

DOIs | |

State | Published - 2001 |

Externally published | Yes |