Quantitative uniqueness for second order elliptic operators with strongly singular coefficients | Zendy

Ching-Lung Lin | Zendy; Gen Nakamura | Zendy; JennNan Wang | Zendy

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Quantitative uniqueness for second order elliptic operators with strongly singular coefficients

Author(s) -

Ching-Lung Lin,

Gen Nakamura,

JennNan Wang

Publication year - 2011

Publication title -

revista matemática iberoamericana

Language(s) - English

Resource type - Journals

SCImago Journal Rank - 1.569

H-Index - 52

eISSN - 2235-0616

pISSN - 0213-2230

DOI - 10.4171/rmi/644

Subject(s) - mathematics , uniqueness , continuation , elliptic operator , order (exchange) , mathematical analysis , property (philosophy) , singular solution , pure mathematics , computer science , philosophy , finance , epistemology , economics , programming language

In this paper we study the local behavior of a solution to second orderelliptic operators with sharp singular coefficients in lower order terms. Oneof the main results is the bound on the vanishing order of the solution, whichis a quantitative estimate of the strong unique continuation property. Ourproof relies on Carleman estimates with carefully chosen phases. A key strategyin the proof is to derive doubling inequalities via three-sphere inequalities.Our method can also be applied to certain elliptic systems with similarsingular coefficients.

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