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On the boundary estimates for second-order elliptic equations

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Abstract Consider uniformly elliptic equations in general form in a domain . We discuss the minimal assumptions on the boundary of which guarantee the existence or non-existence of Hopf–Oleinik estimates… Click to show full abstract

Abstract Consider uniformly elliptic equations in general form in a domain . We discuss the minimal assumptions on the boundary of which guarantee the existence or non-existence of Hopf–Oleinik estimates for solutions, provided . The work is presented in a unified way based on a few basic facts from qualitative theory of elliptic equations.

Keywords: estimates second; second order; equations boundary; elliptic equations; order elliptic; boundary estimates

Journal Title: Complex Variables and Elliptic Equations
Year Published: 2018

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