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- W2340631036 abstract "where Ω is a bounded, open subset of IR , with N > 2, a(x) and A(x) are measurable matrices such that, for α, β ∈ IR, (1.2) α|ξ| ≤ a(x)ξξ, α|ξ| ≤ A(x)ξξ; | a(x)| ≤ β, |A(x)| ≤ β. Moreover we assume (1.3) 0 < λ ≤ b(x), B(x) ≤ γ, for some λ, γ ∈ IR and (1.4) f(x), F (x) ∈ L(Ω). Theorem 1.1. Under the assumptions (1.2), (1.3), (1.4), there exist u ∈ W 1,1 0 (Ω) and z ∈ W 1,1 0 (Ω), distributional solutions of the system (1.1). 1.2. Comments. First of all, we note that existence of solutions belonging to the nonreflexive space W 1,1 0 (Ω) is not so usual in the study of elliptic problems. Recently the existence of solutions in W 1,1 0 (Ω) was proved in [3], [4], [5], for elliptic scalar problems with degenerate coercivity (so that this paper is an extension to the systems of some of those results) and in some borderline cases of the Calderon-Zygmund theory of nonlinear Dirichlet problems in [9]. The main difficulty of the problem is that even if the differential operator is well defined between W 1,2 0 (Ω) and its dual, it is not coercive on W 1,2 0 (Ω): degenerate coercivity means that when |v| is “large”, 1 (b(x)+|v|) goes to zero: for an explicit example see [18]. 1 (see [14], [15], [6], [7],[13], [16], [17],)" @default.
- W2340631036 created "2016-06-24" @default.
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- W2340631036 date "2015-01-01" @default.
- W2340631036 modified "2023-10-03" @default.
- W2340631036 title "An elliptic system with degenerate coercivity" @default.
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