奇异半线性问题的正则化效应

IF 1.6 3区数学 Q1 MATHEMATICS Mathematical Modelling and Analysis Pub Date : 2023-10-20 DOI:10.3846/mma.2023.18616

José Carmona, Antonio J. Martínez Aparicio, Pedro J. Martínez-Aparicio Martínez-Aparicio, Miguel Martínez-Teruel

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引用次数: 0

摘要

我们分析了低阶项中的不同关系如何在奇异问题上导致相同的正则化效果，其模型在Ω， u = 0在∂Ω上，其中Ω是L1(Ω)中的有界开集，是一个非负函数，g(x,s)是一个carathsamodory函数。在不期望解的框架中，只要基准f与域边界或与低阶项方便地相互作用，我们就证明了它的存在性(正则化效应)。

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REGULARIZING EFFECT IN SINGULAR SEMILINEAR PROBLEMS

We analyze how different relations in the lower order terms lead to the same regularizing effect on singular problems whose model is in Ω, u = 0 on ∂Ω, where Ω is a bounded open set of is a nonnegative function in L1(Ω) and g(x,s) is a Carathéodory function. In a framework where no solution is expected, we prove its existence (regularizing effect) whenever the datum f interacts conveniently either with the boundary of the domain or with the lower order term.

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