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Measure Data Problems for a Class of Elliptic Equations with Mixed Absorption-Reaction
Advanced Nonlinear Studies ( IF 1.8 ) Pub Date : 2021-05-01 , DOI: 10.1515/ans-2021-2124
Marie-Françoise Bidaut-Véron 1 , Marta Garcia-Huidobro 2 , Laurent Véron 1
Affiliation  

In the present paper, we study the existence of nonnegative solutions to the Dirichlet problem ℒp,qM⁢u:=-Δ⁢u+up-M⁢|∇⁡u|q=μ{{\mathcal{L}}^{{M}}_{p,q}u:=-\Delta u+u^{p}-M|\nabla u|^{q}=\mu} in a domain Ω⊂ℝN{\Omega\subset\mathbb{R}^{N}} where μ is a nonnegative Radon measure, when p>1{p>1}, q>1{q>1} and M≥0{M\geq 0}. We also give conditions under which nonnegative solutions of ℒp,qM⁢u=0{{\mathcal{L}}^{{M}}_{p,q}u=0} in Ω∖K{\Omega\setminus K}, where K is a compact subset of Ω, can be extended as a solution of the same equation in Ω.

中文翻译:

一类具有混合吸收反应的椭圆方程的测量数据问题

本文研究Dirichlet问题ℒp,qM⁢u:=-Δ⁢u+up-M⁢|∇⁡u| q =μ{{\ mathcal {L}} ^ { {M}} _ {p,q} u:=-\ Delta u + u ^ {p} -M | \ nabla u | ^ {q} = \ mu}在Ω⊂ℝN{\ Omega \ subset \ mathbb {R} ^ {N}}其中,μ是非负Radon量度,当p> 1 {p> 1},q> 1 {q> 1}且M≥0{M \ geq 0}时。我们还给出了在ΩℒK{\ Omega \ setminus K中,ℒp,qM⁢u= 0 {{\ mathcal {L}} ^ {{M}} _ {p,q} u = 0}的非负解的条件},其中K是Ω的紧凑子集,可以扩展为Ω中相同方程的解。
更新日期:2021-04-29
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