一类带有退化强制项的奇异椭圆方程解的存在性

Abstract

Abstract: In this article, the authors consider the existence of solutions for the following elliptic boundary value problem with degenerate coercivity and a singular lower order term with natural growth with respect to the gradient of the following form
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where Ω⊂R^N(N ≥ p) is a bounded domain, B,γ,θ>0 and p > 1, and f is a non-negative function belonging to some Lebesgue space L^m(Ω) with m ≥ 1. By combining the truncation methods with several delicate test functions, the existence and regularity of solution is proved. The results show that the lower order term has some regularizing effects on the solution, even if it is singular.

Key words: Degenerate coercivity, Singularity, Lower order term, Existence, Regularity

CLC Number:

O175.2

Li Qingwei, Gao Wenjie, Han Yuzhu. Existence of Solutions to Some Singular Elliptic Problems with Degenerate Coercivity[J].Acta mathematica scientia,Series A, 2017, 37(5): 877-894.

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References

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Existence of Solutions to Some Singular Elliptic Problems with Degenerate Coercivity

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