Nonuniqueness for some linear oblique derivative problems for elliptic equations

Abstract

It is well-known that the “standard” oblique derivative problem, ∆u = 0 in Ω, ∂u/∂ν − u = 0 on ∂Ω (ν is the unit inner normal) has a unique solution even when the boundary condition is not assumed to hold on the entire boundary. When the boundary condition is modified to satisfy an obliqueness condition, the behavior at a single boundary point can change… (More)

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