p-调和方程在次线性增长下的Liouville定理

Liouville Theorem for p-Harmonic Equation under the Sublinear Growth

为了将将原有经典的有界性假设减弱为次线性增长,文中利用迭代技巧给出了p-调和方程的弱解满足次线性增长时的Liouville型定理,通过选取合适的试验函数,借助H9lder不等式和Sobolev嵌入来进行放缩处理并加以证明,使其能够在更广的空间研究问题,对同类型问题具有指导意义.

In order to reduces the classical assumption of boundedness to sublinear growth,the Liouville theorem for the p-harmonic equation whose weak solutions satisfy the sublinear growth condition is presented by the iterative method.It is proved through scaling by selecting the appropriate test functions and using the H9 lder inequality and Sobolev embedding,which has a certain guiding significance for the same type problem,and can study the problem in a wider space.