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Interior estimates for second-order elliptic differential (or finite-difference) equations via the maximum principle

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Abstract

Second-order elliptic operators are transformed into second-order elliptic operators of a higher dimensionality acting on differences of functions. Applying the maximum principle to the resulting operators yields various a-priori pointwise estimates to difference-quotients of solutions of elliptic differential, as well as finite-difference, equations. We derive Schauder estimates, estimates for equations with discontinuous coefficients, and other estimates.

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Authors and Affiliations

  1. The Weizmann Institute of Science, Rehovot

    A. Brandt

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  1. A. Brandt
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Brandt, A. Interior estimates for second-order elliptic differential (or finite-difference) equations via the maximum principle. Israel J. Math. 7, 95–121 (1969). https://doi.org/10.1007/BF02771657

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