半线性3重调和算子的Hardy不等式

The Hardy Inequality of the Semilinear Operator（-Δ）~3

采用变分不等式对3重调和算子(-Δ)3的Dirichlet边界问题的第一Hardy不等式进行了研究,首次证明了该不等式在全空间的最佳常数,并给出了达到函数.该不等式为相应的反应-扩散方程的解的渐进性的研究提供了一个工具.

The first Hardy inequality for the sixth order qusilinear elliptic equations is studied by the variational inequalities.The optimal constant of the Hardy inequality in the total space RN is obtained and the reaching function is founded.The inequality supplies a tool for studying the approaching attribute of the solutions for the reaction-diffusion equations.