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

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Abstract

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| 1 (log |x|)2 exp( β/2 (log |x|)2).

Original languageEnglish
Pages (from-to)569-578
Number of pages10
JournalProceedings of the American Mathematical Society
Volume135
Issue number2
DOIs
Publication statusPublished - 2007 Feb 1

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Singular Coefficients
Carleman Estimate
Unique Continuation
Theorem
Form

All Science Journal Classification (ASJC) codes

  • Mathematics(all)
  • Applied Mathematics

Cite this

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abstract = "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).",
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