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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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