Dept. Math, Hokkaido Univ. EPrints Server

The boundary growth of superharmonic functions and positive solutions of nonlinear elliptic equations

Preprint Series # 814
Hirata, Kentaro The boundary growth of superharmonic functions and positive solutions of nonlinear elliptic equations. (2006);

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Abstract

We investigate the boundary growth of positive superharmonic functions on a bounded domain satisfying a certain nonlinear elliptic inequality. The result is applied to show the Harnack inequality for such superharmonic functions. Also, we study the existence of positive solutions, with singularity on the boundary, of elliptic equations with nonlinear term conditioned by the generalized Kato class.

Item Type:Preprint
Additional Information:30
Uncontrolled Keywords:boundary growth, superharmonic function, nonlinear elliptic equation
Subjects:31-xx POTENTIAL THEORY
ID Code:1637