### 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 |
---|---|

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 Jan 1 |

Externally published | Yes |

### Fingerprint

### Keywords

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

### ASJC Scopus subject areas

- Analysis
- Computational Mathematics
- Applied Mathematics

### Cite this

^{p}norms.

*SIAM Journal on Mathematical Analysis*,

*33*(3), 545-569. https://doi.org/10.1137/S0036141000380000

**On fully nonlinear PDEs derived from variational problems of L ^{p} norms.** / Ishibashi, Toshihiro; Koike, Shigeaki.

Research output: Contribution to journal › Article

^{p}norms',

*SIAM Journal on Mathematical Analysis*, vol. 33, no. 3, pp. 545-569. https://doi.org/10.1137/S0036141000380000

^{p}norms. SIAM Journal on Mathematical Analysis. 2001 Jan 1;33(3):545-569. https://doi.org/10.1137/S0036141000380000

}

TY - JOUR

T1 - On fully nonlinear PDEs derived from variational problems of Lp norms

AU - Ishibashi, Toshihiro

AU - Koike, Shigeaki

PY - 2001/1/1

Y1 - 2001/1/1

N2 - The p-Laplace operator arises in the Euler-Lagrange equation associated with a minimizing problem which contains the Lpnorm of the gradient of functions. However, when we adapt a different Lpnorm 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.

AB - The p-Laplace operator arises in the Euler-Lagrange equation associated with a minimizing problem which contains the Lpnorm of the gradient of functions. However, when we adapt a different Lpnorm 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.

KW - Comparison principle

KW - Concave solution

KW - Fully nonlinear equation

KW - Viscosity solution

KW - ∞-Laplacian

UR - http://www.scopus.com/inward/record.url?scp=0036345362&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=0036345362&partnerID=8YFLogxK

U2 - 10.1137/S0036141000380000

DO - 10.1137/S0036141000380000

M3 - Article

AN - SCOPUS:0036345362

VL - 33

SP - 545

EP - 569

JO - SIAM Journal on Mathematical Analysis

JF - SIAM Journal on Mathematical Analysis

SN - 0036-1410

IS - 3

ER -