Consider uniformly elliptic equations in general form Lu = aijDiju + biDiui n a domain Ω ⊂ Rn, n ≥ 2.. We discuss the minimal assumptions on the boundary of Ω which guarantee the existence or non-existence of Hopf–Oleinik estimates for solutions, provided bi ∈ Lq(Ω),q > n.. The work is presented in a unified way based on a few basic facts from qualitative theory of elliptic equations.
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- Elliptic equations
- Hopf–Oleinik lemma
- measurable coefficients