## Abstract

The p-Laplace operator arises in the Euler-Lagrange equation associated with a minimizing problem which contains the L^{p}norm of the gradient of functions. However, when we adapt a different L^{p}norm equivalent to the standard one in the minimizing problem, a different p-Laplace-type operator appears in the corresponding Euler-Lagrange equation. First, we derive the limit PDE which the limit function of minimizers of those, as p → ∞, satisfies in the viscosity sense. Then we investigate the uniqueness and existence of viscosity solutions of the limit PDE.

Original language | English |
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Pages (from-to) | 545-569 |

Number of pages | 25 |

Journal | SIAM Journal on Mathematical Analysis |

Volume | 33 |

Issue number | 3 |

DOIs | |

Publication status | Published - 2001 |

Externally published | Yes |

## Keywords

- Comparison principle
- Concave solution
- Fully nonlinear equation
- Viscosity solution
- ∞-Laplacian

## ASJC Scopus subject areas

- Analysis
- Computational Mathematics
- Applied Mathematics

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