### Abstract

In this paper we prove strong unique continuation for u satisfying an inequality of the form |δ^{m}u| ≤ f(x, u,Du, ⋯ ,D ^{k}u), where k is up to [3m/2]. This result gives an improvement of a work by Colombini and Grammatico (1999) in some sense. The proof of the main theorem is based on Carleman estimates with three-parameter weights |x| ^{2σ}_{1} (log |x|)^{2σ}_{2} exp( β/2 (log |x|)^{2}).

Original language | English |
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Pages (from-to) | 569-578 |

Number of pages | 10 |

Journal | Proceedings of the American Mathematical Society |

Volume | 135 |

Issue number | 2 |

DOIs | |

Publication status | Published - 2007 Feb 1 |

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### All Science Journal Classification (ASJC) codes

- Mathematics(all)
- Applied Mathematics

### Cite this

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**Strong unique continuation for m-th powers of a laplacian operator with singular coefficients.** / Lin, Ching-Lung.

Research output: Contribution to journal › Article

TY - JOUR

T1 - Strong unique continuation for m-th powers of a laplacian operator with singular coefficients

AU - Lin, Ching-Lung

PY - 2007/2/1

Y1 - 2007/2/1

N2 - In this paper we prove strong unique continuation for u satisfying an inequality of the form |δmu| ≤ f(x, u,Du, ⋯ ,D ku), where k is up to [3m/2]. This result gives an improvement of a work by Colombini and Grammatico (1999) in some sense. The proof of the main theorem is based on Carleman estimates with three-parameter weights |x| 2σ1 (log |x|)2σ2 exp( β/2 (log |x|)2).

AB - In this paper we prove strong unique continuation for u satisfying an inequality of the form |δmu| ≤ f(x, u,Du, ⋯ ,D ku), where k is up to [3m/2]. This result gives an improvement of a work by Colombini and Grammatico (1999) in some sense. The proof of the main theorem is based on Carleman estimates with three-parameter weights |x| 2σ1 (log |x|)2σ2 exp( β/2 (log |x|)2).

UR - http://www.scopus.com/inward/record.url?scp=77950656314&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=77950656314&partnerID=8YFLogxK

U2 - 10.1090/S0002-9939-06-08740-5

DO - 10.1090/S0002-9939-06-08740-5

M3 - Article

VL - 135

SP - 569

EP - 578

JO - Proceedings of the American Mathematical Society

JF - Proceedings of the American Mathematical Society

SN - 0002-9939

IS - 2

ER -