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A proof of Khavinson's conjecture in $\mathbf{R}^4$
| Content Provider | Semantic Scholar |
|---|---|
| Author | Kalaj, David |
| Copyright Year | 2016 |
| Abstract | The paper deals with an extremal problem for bounded harmonic functions in the unit ball of $\mathbf{R}^4$. We solve the generalized Khavinson problem in $\mathbf{R}^4$. This precise problem was formulated by G. Kresin and V. Maz'ya for harmonic functions in the unit ball and in the half--space of $\mathbf{R}^n$. We find the optimal pointwise estimates for the norm of the gradient of bounded real--valued harmonic functions. |
| File Format | PDF HTM / HTML |
| Alternate Webpage(s) | https://arxiv.org/pdf/1601.03347v1.pdf |
| Language | English |
| Access Restriction | Open |
| Content Type | Text |
| Resource Type | Article |