The L resolvents of elliptic operators with uniformly continuous coefficients |
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Authors: | Yoichi Miyazaki |
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Institution: | School of Dentistry, Nihon University, 8-13, Kanda-Surugadai 1-chome, Chiyoda-ku, Tokyo 101-8310, Japan |
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Abstract: | We consider the strongly elliptic operator A of order 2m in the divergence form with bounded measurable coefficients and assume that the coefficients of top order are uniformly continuous. For 1<p<∞, A is a bounded linear operator from the Lp Sobolev space Hm,p into H−m,p. We will prove that (A−λ)−1 exists in H−m,p for some λ and estimate its operator norm. |
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Keywords: | Lp theory Elliptic operator Non-smooth coefficient Divergence form Resolvent Uniformly continuous |
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