In this paper we study the local behavior of a solution to the -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.
@article{ASNSP_2011_5_10_3_513_0, 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://www.numdam.org/item/ASNSP_2011_5_10_3_513_0/} }
TY - JOUR AU - Lin, Ching-Lung AU - Nagayasu, Sei AU - Wang, Jenn-Nan TI - Quantitative uniqueness for the power of the Laplacian with singular coefficients JO - Annali della Scuola Normale Superiore di Pisa - Classe di Scienze PY - 2011 SP - 513 EP - 529 VL - 10 IS - 3 PB - Scuola Normale Superiore, Pisa UR - http://www.numdam.org/item/ASNSP_2011_5_10_3_513_0/ LA - en ID - ASNSP_2011_5_10_3_513_0 ER -
%0 Journal Article %A Lin, Ching-Lung %A Nagayasu, Sei %A Wang, Jenn-Nan %T Quantitative uniqueness for the power of the Laplacian with singular coefficients %J Annali della Scuola Normale Superiore di Pisa - Classe di Scienze %D 2011 %P 513-529 %V 10 %N 3 %I Scuola Normale Superiore, Pisa %U http://www.numdam.org/item/ASNSP_2011_5_10_3_513_0/ %G en %F ASNSP_2011_5_10_3_513_0
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://www.numdam.org/item/ASNSP_2011_5_10_3_513_0/
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