Parabolic approach to nonlinear elliptic eigenvalue problems
Parabolic approach to nonlinear elliptic eigenvalue problems
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DOI：
10.1016/j.aim.2008.07.012
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发表时间：
2008-12
影响因子：
1.7
通讯作者：
Ki-ahm Lee;J. Vázquez
中科院分区：
文献类型：
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作者：
Ki-ahm Lee;J. Vázquez
我们考虑非线性抛物流ut=Δ um的渐近分布，以显示下列椭圆非线性特征值问题的几何性质：在p=1的经典情况下，我们建立log（φ）是严格凹函数，当0<p<1时，函数φ1− p2是严格凹的，而对于1<p<n+2n−2，至少有一个解使得φ1− p2是严格凸的。此外，最终凸性性质的抛物流被证明。
We consider the asymptotic profiles of the nonlinear parabolic flows ut=Δumto show the geometric properties of the following elliptic nonlinear eigenvalue problems: posed in a strictly convex domain Ω⊂Rnfor different values of p. In the classical case p=1 we establish that log(φ) is a strictly concave function, when 0<p<1 the function φ1−p2is strictly concave, while for 1<p<n+2n−2 there is at least a solution such that φ1−p2is strictly convex. Moreover, eventual convexity properties for the parabolic flows are proved.