@article {2001,
title = {A monotonicity approach to nonlinear Dirichlet problems in perforated domains},
journal = {Adv. Math. Sci. Appl. 11 (2001) 721-751},
number = {SISSA;99/00/M},
year = {2001},
publisher = {SISSA Library},
abstract = {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.},
url = {http://hdl.handle.net/1963/1555},
author = {Gianni Dal Maso and Igor V. Skrypnik}
}
@article {1999,
title = {Asymptotic behaviour of nonlinear elliptic higher order equations in perforated domains},
journal = {Journal d\\\'Analyse Mathematique, Volume 79, 1999, Pages: 63-112},
year = {1999},
isbn = {1618-1891},
doi = {10.1007/BF01759365},
url = {http://hdl.handle.net/1963/6433},
author = {Gianni Dal Maso and Igor V. Skrypnik}
}
@article {1998,
title = {Asymptotic behavior of nonlinear Dirichlet problems in perforated domains},
journal = {Ann. Mat. Pura Appl. (4) 174 (1998), 13--72},
number = {SISSA;162/95/M},
year = {1998},
publisher = {SISSA Library},
url = {http://hdl.handle.net/1963/1064},
author = {Gianni Dal Maso and Igor V. Skrypnik}
}
@article {1997,
title = {Capacity theory for monotone operators},
journal = {Potential Anal. 7 (1997), no. 4, 765-803},
number = {SISSA;6/95/M},
year = {1997},
publisher = {Springer},
abstract = {If $Au=-div(a(x,Du))$ is a monotone operator defined on the Sobolev space $W^{1,p}(R^n)$, $1< p <+\\\\infty$, with $a(x,0)=0$ for a.e. $x\\\\in R^n$, the capacity $C_A(E,F)$ relative to $A$ can be defined for every pair $(E,F)$ of bounded sets in $R^n$ with $E\\\\subset F$. We prove that $C_A(E,F)$ is increasing and countably subadditive with respect to $E$ and decreasing with respect to $F$. Moreover we investigate the continuity properties of $C_A(E,F)$ with respect to $E$ and $F$.},
doi = {10.1023/A:1017987405983},
url = {http://hdl.handle.net/1963/911},
author = {Gianni Dal Maso and Igor V. Skrypnik}
}