We study the limit as n goes to +∞ of the renormalized solutions un to the nonlinear elliptic problems −div (a_n(x,∇u_n)) = μ, in E , u_n = 0 on ∂E, where E is a bounded open set of R^N , N ≥ 2, and μ is a Radon measure with bounded variation in E. Under the assumption of G-convergence of the operators A_n(v) = −div (a_n(x,∇v)), defined for v ∈ W^{1,p}_0 (E), p > 1, to the operator A0(v) = −div (a0(x,∇v)), we shall prove that the sequence (u_n) admits a subsequence converging almost everywhere in E to a function u which is a renormalized solution to the problem −div (a0(x,∇u)) = μ in E, u = 0 on ∂E.
Asymptotic behaviour of renormalized solutions to elliptic equations with measure data and G-converging operators / Malusa, Annalisa; Orsina, Luigi. - In: CALCULUS OF VARIATIONS AND PARTIAL DIFFERENTIAL EQUATIONS. - ISSN 0944-2669. - 27:2(2006), pp. 179-202. [10.1007/s00526-006-0008-2]
Asymptotic behaviour of renormalized solutions to elliptic equations with measure data and G-converging operators
MALUSA, ANNALISA;ORSINA, Luigi
2006
Abstract
We study the limit as n goes to +∞ of the renormalized solutions un to the nonlinear elliptic problems −div (a_n(x,∇u_n)) = μ, in E , u_n = 0 on ∂E, where E is a bounded open set of R^N , N ≥ 2, and μ is a Radon measure with bounded variation in E. Under the assumption of G-convergence of the operators A_n(v) = −div (a_n(x,∇v)), defined for v ∈ W^{1,p}_0 (E), p > 1, to the operator A0(v) = −div (a0(x,∇v)), we shall prove that the sequence (u_n) admits a subsequence converging almost everywhere in E to a function u which is a renormalized solution to the problem −div (a0(x,∇u)) = μ in E, u = 0 on ∂E.I documenti in IRIS sono protetti da copyright e tutti i diritti sono riservati, salvo diversa indicazione.
