奇异非线性Dirichlet问题中低阶项的影响

IF 0.5 4区数学 Q3 MATHEMATICS

Portugaliae Mathematica Pub Date : 2020-07-15 DOI:10.4171/PM/2041

L. Boccardo, G. Croce

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引用次数: 9

摘要

本文研究了以下Dirichlet问题−div(a(x)|∇u| p−2∇u) + u|u| r−1 = f (x) u θ在Ω中，u >在Ω中，u = 0在∂Ω中，证明了低阶项u|u| r−1对解有一定的正则化作用。数学学科分类(2010)。35 j66 35 j75

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The impact of a lower order term in a Dirichlet problem with a singular nonlinearity

In this paper we study the existence and regularity of solutions to the following Dirichlet problem        −div(a(x)|∇u| p−2 ∇u) + u|u| r−1 = f (x) u θ in Ω, u > 0 in Ω, u = 0 on ∂Ω proving that the lower order term u|u| r−1 has some regularizing effects on the solutions. Mathematics Subject Classification (2010). 35J66, 35J75

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来源期刊

Portugaliae Mathematica MATHEMATICS, APPLIED-MATHEMATICS

CiteScore

0.90

自引率

12.50%

发文量

审稿时长

>12 weeks

期刊介绍： Since its foundation in 1937, Portugaliae Mathematica has aimed at publishing high-level research articles in all branches of mathematics. With great efforts by its founders, the journal was able to publish articles by some of the best mathematicians of the time. In 2001 a New Series of Portugaliae Mathematica was started, reaffirming the purpose of maintaining a high-level research journal in mathematics with a wide range scope.