RT Journal Article
T1 Existence and regularity of renormalized solutions for some elliptic problems involving derivatives of nonlinear terms
A1 Díaz Díaz, Jesús Ildefonso
A1 Boccardo, L.
A1 Giachetti, D.
A1 Murat, F.
AB The authors study the nonlinear elliptic equation (*) −div(a(x,u,Du))−div(Φ(u))+g(x,u)=f(x)in Ωwith 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.
PB Elsevier
SN 0022-0396
YR 1993
FD 1993-11
LK https://hdl.handle.net/20.500.14352/57484
UL https://hdl.handle.net/20.500.14352/57484
LA eng
DS Docta Complutense
RD 6 abr 2025