Local Uniqueness in the Cauchy Problem for Second Order Elliptic Equations with Non-Lipschitzian Coefficients | Zendy

Shigeo Tarama | Zendy

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Local Uniqueness in the Cauchy Problem for Second Order Elliptic Equations with Non-Lipschitzian Coefficients

Author(s) -

Shigeo Tarama

Publication year - 1997

Publication title -

publications of the research institute for mathematical sciences

Language(s) - English

Resource type - Journals

SCImago Journal Rank - 0.786

H-Index - 39

eISSN - 1663-4926

pISSN - 0034-5318

DOI - 10.2977/prims/1195145537

Subject(s) - mathematics , uniqueness , modulus of continuity , principal part , lipschitz continuity , hölder condition , cauchy distribution , mathematical analysis , order (exchange) , cauchy problem , modulus , pure mathematics , initial value problem , type (biology) , geometry , ecology , finance , economics , biology

We show the local uniqueness of the Cauchy problem for the second order elliptic operators whose coefficients of the principal part are real-valued and continuous with some modulus of continuity. These coefficients are not necessarily lipschitz continuous. The proof is given by drawing the Carleman estimates with a weight attached to the modulus of continuity. §

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