Measure Estimates of Nodal Sets of Polyharmonic Functions

Citation:

Long TIAN.Measure Estimates of Nodal Sets of Polyharmonic Functions[J].Chinese Annals of Mathematics B,2018,39(5):917~932
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Authors:

Long TIAN;

Foundation:

This work was supported by the National Natural Science Foundation of China (Nos.11401307, 1150 1292).
Abstract: This paper deals with the function $u$ which satisfies $\triangle^ku=0$, where $k\geq2$ is an integer. Such a function $u$ is called a polyharmonic function. The author gives an upper bound of the measure of the nodal set of $u$, and shows some growth property of $u$.

Keywords:

Polyharmonic function, Nodal set, Frequency, Measure estimate,Growth property

Classification:

58E10, 53C50
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