2024-03-04T05:57:24Zhttps://eprints.lib.hokudai.ac.jp/dspace-oai/requestoai:eprints.lib.hokudai.ac.jp:2115/693022022-11-17T02:08:08Zhdl_2115_45007hdl_2115_116Berg's effectGiga, Y.Rybka, P.open access410A Neumann problem for the Laplace equation is considered outside a three dimensional straight cylinder. The value of a solution O" at space infinity is prescribed. The Neumann data aO" / an ( n is the outer normal of the cylinder) is assumed to be independent of the spatial variables on the top and the bottom and also on the lateral part of the boundary of the cylinder. The behavior of the value of O" on the boundary is studied. In particular, it is shown that O" is an increasing function of the distance from the center of the top ( respectively, the bottom) if a(J" / an > o on the lateral part and a(J" / an is the same constant on the top and (respectively, the bottom). An analogous statement is shown for O" on the lateral part. In the theory of crystal growth O" is interpreted as a supersaturation and cylinder is a crystal. The value aO" / an is the growth speed. The main contribution of this paper is considered as the first rigorous proof of Berg's effect when the crystal shape is a cylinder.Department of Mathematics, Hokkaido University2002-07engdepartmental bulletin paperVoRhttps://doi.org/10.14943/83698http://hdl.handle.net/2115/6930210.14943/83698Hokkaido University Preprint Series in Mathematics553112https://eprints.lib.hokudai.ac.jp/dspace/bitstream/2115/69302/1/pre553.pdfapplication/pdf591.41 KB2002-07