On convexity and starshapedness of level sets for some nonlinear elliptic and parabolic problems on convex rings
On convexity and starshapedness of level sets for some nonlinear elliptic and parabolic problems on convex rings
复制标题
凸环上一些非线性椭圆和抛物线问题的水平集的凸性和星形性
DOI：
10.1006/jmaa.1993.1257
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发表时间：
1993
影响因子：
1.3
通讯作者：
B. Kawohl
中科院分区：
文献类型：
--
作者：
J. I. Díaz;B. Kawohl
“我们考虑凸环（或星形环）上的一些退化抛物问题。我们证明了如果初始数据具有凸（或星形）水平集，则解u（t,⋅）对于任意正t具有相同的性质。对于相应的平稳问题也显示了类似的结果。我们的结果特别暗示了某些自由边界的凹凸性（或星形性）。对其他非线性抛物问题也进行了讨论。
"We consider some degenerate parabolic problems on a convex (or starshaped) ring. We prove that if the initial data have convex (or starshaped) level sets, then the solution u(t,⋅) has the same property for any positive t. Similar results are shown for the corresponding stationary problems. Our results imply in particular the convexity (or starshapedness) of certain free boundaries. Other nonlinear parabolic problems are also discussed.''