Geodesic
Quantitative uniqueness for the power of the Laplacian with singular coefficients
Lin, Ching-Lung1 ; Nagayasu, Sei2 ; Wang, Jenn-Nan3
1 Department of Mathematics NCTS, National Cheng Kung University Tainan 701, Taiwan
2 Department of Mathematics Taida Institute for Mathematical Sciences National Taiwan University Taipei 106, Taiwan
3 Department of Mathematics Taida Institute of Mathematical Sciences NCTS (Taipei), National Taiwan University Taipei 106, Taiwan
Annali della Scuola Normale Superiore di Pisa - Classe di Scienze, Série 5, Tome 10 (2011) no. 3, pp. 513-529

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In this paper we study the local behavior of a solution to the l-th power of the Laplacian with singular coefficients in lower order terms. We obtain a bound on the vanishing order of the nontrivial solution. Our proofs use Carleman estimates with carefully chosen weights. We will derive appropriate three-sphere inequalities and apply them to obtain doubling inequalities and the maximal vanishing order.

Publié le :
Classification : 35J15, 35A02

Lin, Ching-Lung 1 ; Nagayasu, Sei 2 ; Wang, Jenn-Nan 3

1 Department of Mathematics NCTS, National Cheng Kung University Tainan 701, Taiwan
2 Department of Mathematics Taida Institute for Mathematical Sciences National Taiwan University Taipei 106, Taiwan
3 Department of Mathematics Taida Institute of Mathematical Sciences NCTS (Taipei), National Taiwan University Taipei 106, Taiwan 
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     author = {Lin, Ching-Lung and Nagayasu, Sei and Wang, Jenn-Nan},
     title = {Quantitative uniqueness for the power of the {Laplacian} with singular coefficients},
     journal = {Annali della Scuola Normale Superiore di Pisa - Classe di Scienze},
     pages = {513--529},
     publisher = {Scuola Normale Superiore, Pisa},
     volume = {Ser. 5, 10},
     number = {3},
     year = {2011},
     mrnumber = {2905377},
     zbl = {1237.35164},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/ASNSP_2011_5_10_3_513_0/}
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Lin, Ching-Lung; Nagayasu, Sei; Wang, Jenn-Nan. Quantitative uniqueness for the power of the Laplacian with singular coefficients. Annali della Scuola Normale Superiore di Pisa - Classe di Scienze, Série 5, Tome 10 (2011) no. 3, pp. 513-529. http://geodesic.mathdoc.fr/item/ASNSP_2011_5_10_3_513_0/