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 -
TY - JOUR
T1 - Asymptotic behaviour of nonlinear elliptic higher order equations in perforated domains
JF - Journal d\\\'Analyse Mathematique, Volume 79, 1999, Pages: 63-112
Y1 - 1999
A1 - Gianni Dal Maso
A1 - Igor V. Skrypnik
SN - 1618-1891
UR - http://hdl.handle.net/1963/6433
U1 - 6374
U2 - Mathematics
U4 - 1
U5 - MAT/05 ANALISI MATEMATICA
ER -
TY - JOUR
T1 - Asymptotic behavior of nonlinear Dirichlet problems in perforated domains
JF - Ann. Mat. Pura Appl. (4) 174 (1998), 13--72
Y1 - 1998
A1 - Gianni Dal Maso
A1 - Igor V. Skrypnik
PB - SISSA Library
UR - http://hdl.handle.net/1963/1064
U1 - 2738
U2 - Mathematics
U3 - Functional Analysis and Applications
ER -
TY - JOUR
T1 - Capacity theory for monotone operators
JF - Potential Anal. 7 (1997), no. 4, 765-803
Y1 - 1997
A1 - Gianni Dal Maso
A1 - Igor V. Skrypnik
AB - 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 $F$.
PB - Springer
UR - http://hdl.handle.net/1963/911
U1 - 2880
U2 - Mathematics
U3 - Functional Analysis and Applications
ER -