JournalsprimsVol. 33, No. 1pp. 167–188

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

  • Shigeo Tarama

    Kyoto University, Japan
Local Uniqueness in the Cauchy Problem for Second Order Elliptic Equations with Non-Lipschitzian Coefficients cover
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Abstract

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.

Cite this article

Shigeo Tarama, Local Uniqueness in the Cauchy Problem for Second Order Elliptic Equations with Non-Lipschitzian Coefficients. Publ. Res. Inst. Math. Sci. 33 (1997), no. 1, pp. 167–188

DOI 10.2977/PRIMS/1195145537