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Nonuniqueness for some linear oblique derivative problems for elliptic equations. (English) Zbl 1064.35508
This paper gives two examples for nonuniqueness of a solution of the oblique derivative problem \(\Delta u=0\) in \(\Omega \), \(\beta _i D_iu+\gamma u=g\) on \(\partial \Omega \), where \(\gamma \) is a continuous nonpositive function, which is not identically zero on \(\partial \Omega \), and \(\beta \) is a vector function such that \(\beta \cdot \nu >0\) for \(\nu \) the unit inner normal to \(\partial G\).

MSC:
35J25 Boundary value problems for second-order elliptic equations
35A05 General existence and uniqueness theorems (PDE) (MSC2000)
35J05 Laplace operator, Helmholtz equation (reduced wave equation), Poisson equation
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