Díaz Díaz, Jesús IldefonsoBoccardo, L.Giachetti, D.Murat, F.2023-06-202023-06-201993-110022-039610.1006/jdeq.1993.1106https://hdl.handle.net/20.500.14352/57484The authors study the nonlinear elliptic equation (*) −div(a(x,u,Du))−div(Φ(u))+g(x,u)=f(x)in Ω with the boundary condition (∗∗) u=0 on ∂Ω, where Ω is a bounded open subset of RN, A(u)=−div(a(x,u,Du)) is a nonlinear operator of Leray-Lions type from W1,p0(Ω) into its dual, Φ∈(C0(R))N, g(x,t)t≥0, and f∈W−1,p′(Ω). No growth hypothesis is assumed on the vector-valued function Φ(u). The term div(Φ(u)) may be meaningless for usual weak solutions, even as a distribution. The authors deal with a weaker form of (∗),(∗∗), solutions of which in W1,p0(Ω) are called the "renormalized solutions'' of the original problem (∗),(∗∗). This weaker form can be formally obtained from (∗) by means of pointwise multiplication by h(u), where h is a C1 function with compact support. They prove the existence of renormalized solutions of (∗),(∗∗) and give sufficient conditions under which a renormalized solution is a usual weak solution. Furthermore, the authors study Ls- and L∞-regularity of renormalized solutions.engjournal articlehttp://www.sciencedirect.com/science/article/pii/S002203968371106Xhttp://www.sciencedirect.com/science/journal/00220396/106/restricted access517.98519.6renormalized solutionsnonlinear Leray-Lions operatorlargest class of possible test functionsAnálisis funcional y teoría de operadoresAnálisis numérico1206 Análisis Numérico