This article proves the existence of a renormalized solution for nonlinear elliptic equations in specific function spaces, indicating important theoretical advancements in mathematics.
In this article, we prove the existence of a renormalised solution to the problem of the nonlinear elliptic equation: {cases} -div ( a(x, u, Du) ) = f & in Ω, \\ u = 0 & on ∂Ω, {cases} , (1) where a(x, u, Du) is blow-up for a finite value m of the unknown u and the data f ∈ L^1(Ω) .
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Fatry et al. (2025) studied this question.
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