## Abstract

We are interested in variational problems of the form min ∝W(∇u) dx, with W nonconvex. The theory of relaxation allows one to calculate the minimum value, but it does not determine a well-defined "solution" since minimizing sequences are far from unique. A natural idea for determining a solution is regularization, i.e. the addition of a higher order term such as ε|∇∇u|^{2}. But what is the behavior of the regularized solution in the limit as ε→0? Little is known in general. Our recent work [19, 20, 21] discusses a particular problem of this type, namely min_{ u y}=±1 ∝∝u_{ x}^{ 2} +ε|u_{ yy}|dxdy with various boundary conditions. The present paper gives an expository overview of our methods and results.

Original language | English (US) |
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Pages (from-to) | 89-113 |

Number of pages | 25 |

Journal | Rendiconti del Seminario Matematico e Fisico di Milano |

Volume | 62 |

Issue number | 1 |

DOIs | |

State | Published - Dec 1992 |

## ASJC Scopus subject areas

- Mathematics(all)
- Physics and Astronomy(all)