Electron. J. Diff. Equ., Vol. 2015 (2015), No. 305, pp. 1-16.

Nonlinear elliptic equations with general growth in the gradient related to Gauss measure

Yujuan Tian, Chao Ma, Fengquan Li

In this article, we establish a comparison result through symmetrization for solutions to some problems with general growth in the gradient. This allows to get sharp estimates for the solutions, obtained by comparing them with solutions of simpler problems whose data depend only on the first variable. Furthermore, we use such result to prove the existence of bounded solutions. All the above results are based on the study of a class of nonlinear integral operator of Volterra type.

Submitted July 22, 2015. Published December 16, 2015.
Math Subject Classifications: 35J60, 35J70, 35J15.
Key Words: Comparison results; symmetrization; gauss measure; nonlinear elliptic equation.

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Yujuan Tian
School of Mathematical Sciences
Shandong Normal University
Jinan 250014, China
email: tianyujuan0302@126.com
Chao Ma
School of Mathematical Sciences
University of Jinan
Jinan 250022, China
email: chaos_ma@163.com
Fengquan Li
School of Mathematical Sciences
Dalian University of Technology
Dalian 116024, China
email: fqli@dlut.edu.cn

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