Reduced limit for semilinear boundary value problems with measure data |
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Authors: | Mousomi Bhakta Moshe Marcus |
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Institution: | Department of Mathematics, Technion, Haifa 32000, Israel |
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Abstract: | We study boundary value problems for semilinear elliptic equations of the form −Δu+g°u=μ in a smooth bounded domain Ω⊂RN. Let {μn} and {νn} be sequences of measure in Ω and ∂Ω respectively. Assume that there exists a solution un with data (μn,νn), i.e., un satisfies the equation with μ=μn and has boundary trace νn. Further assume that the sequences of measures converge in a weak sense to μ and ν respectively while {un} converges to u in L1(Ω). In general u is not a solution of the boundary value problem with data (μ,ν). However there exists a pair of measures (μ?,ν?) such that u is a solution of the boundary value problem with this data. The pair (μ?,ν?) is called the reduced limit of the sequence {(μn,νn)}. We investigate the relation between the weak limit and the reduced limit and the dependence of the latter on the sequence. A closely related problem was studied by Marcus and Ponce 3]. |
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Keywords: | 35J25 35J61 |
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