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Let C0 be a curve in a disk D = {|z| < 1} tangential to a circle at the point z = 1 and let Cθ be the result of… Click to show full abstract
Let C0 be a curve in a disk D = {|z| < 1} tangential to a circle at the point z = 1 and let Cθ be the result of rotation of this curve by an angle θ about the origin z = 0. We construct a bounded function u(z) three-harmonic in D with zero normal derivatives ∂u∂nand∂2u∂r2$$ \frac{\partial u}{\partial n}\mathrm{and}\frac{\partial^2u}{\partial {r}^2} $$ on the boundary such that the limit along Cθ does not exist for all θ, 0 ≤ θ ≤ 2π.
Keywords:
values three;
harmonic poisson;
three harmonic;
integral boundary;
boundary values;
poisson integral
Journal Title: Ukrainian Mathematical Journal
Year Published: 2018
Link to full text (if available)
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Journal Title: Ukrainian Mathematical Journal
Year Published: 2018
Link to full text (if available)
Share on Social Media: Sign Up to like & get
recommendations!