THE EXPONENTIAL PROPERTY OF SOLUTIONS BOUNDED FROM BELOW TO DEGENERATE EQUATIONS IN UNBOUNDED DOMAINS

doi:10.1007/s10473-022-0118-8

Acta mathematica scientia,Series B ›› 2022, Vol. 42 ›› Issue (1): 323-348.doi: 10.1007/s10473-022-0118-8

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THE EXPONENTIAL PROPERTY OF SOLUTIONS BOUNDED FROM BELOW TO DEGENERATE EQUATIONS IN UNBOUNDED DOMAINS

Lidan WANG

School of Mathematical Sciences, Shanghai Jiao Tong University, Shanghai, 200240, China

Received:2020-06-04 Revised:2021-05-21 Online:2022-02-25 Published:2022-02-24
Supported by:
The author was supported partially by NSFC (11771285).

Abstract

Abstract: This paper is focused on studying the structure of solutions bounded from below to degenerate elliptic equations with Neumann and Dirichlet boundary conditions in unbounded domains. After establishing the weak maximum principles, the global boundary Hölder estimates and the boundary Harnack inequalities of the equations, we show that all solutions bounded from below are linear combinations of two special solutions (exponential growth at one end and exponential decay at the other) with a bounded solution to the degenerate equations.

Key words: degenerate elliptic equations, unbounded domains, boundary Harnack inequalities

CLC Number:

36J65

Lidan WANG. THE EXPONENTIAL PROPERTY OF SOLUTIONS BOUNDED FROM BELOW TO DEGENERATE EQUATIONS IN UNBOUNDED DOMAINS[J].Acta mathematica scientia,Series B, 2022, 42(1): 323-348.

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THE EXPONENTIAL PROPERTY OF SOLUTIONS BOUNDED FROM BELOW TO DEGENERATE EQUATIONS IN UNBOUNDED DOMAINS

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