Volume 23, Issue 4
Uniqueness of the Weak Extremal Solution to Biharmonic Equation with Logarithmically Convex Nonlinearities

Xue Luo

10.4208/jpde.v23.n4.2

J. Part. Diff. Eq., 23 (2010), pp. 315-329.

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  • Abstract

In this note, we investigate the existence of the minimal solution and the uniqueness of the weak extremal (probably singular) solution to the biharmonic equation Δ^2ω=λg(ω) with Dirichlet boundary condition in the unit ball in R^n, where the source term is logarithmically convex. An example is also given to illustrate that the logarithmical convexity is not a necessary condition to ensure the uniqueness of the extremal solution.

  • History

Published online: 2010-11

  • AMS Subject Headings

35G30, 35J40

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