TY - JOUR
T1 - A monotonicity approach to nonlinear Dirichlet problems in perforated domains
JF - Adv. Math. Sci. Appl. 11 (2001) 721-751
Y1 - 2001
A1 - Gianni Dal Maso
A1 - Igor V. Skrypnik
AB - We study the asymptotic behaviour of solutions to Dirichlet problems in perforated domains for nonlinear elliptic equations associated with monotone operators. The main difference with respect to the previous papers on this subject is that no uniformity is assumed in the monotonicity condition. Under a very general hypothesis on the holes of the domains, we construct a limit equation, which is satisfied by the weak limits of the solutions. The additional term in the limit problem depends only on the local behaviour of the holes, which can be expressed in terms of suitable nonlinear capacities associated with the monotone operator.
PB - SISSA Library
UR - http://hdl.handle.net/1963/1555
U1 - 2563
U2 - Mathematics
U3 - Functional Analysis and Applications
ER -