TY - JOUR
T1 - Mosco-convergence and Wiener measures for conductive thin boundaries
AU - Masamune, Jun
N1 - Funding Information:
This work is partially supported by the National Science Foundation No. 0807840. E-mail address: jum35@psu.edu. 1 This is one of the standard models in the study of super conductivity.
PY - 2011/12/15
Y1 - 2011/12/15
N2 - The Mosco-convergence of energy functionals and the convergence of associated Wiener measures are proved for a domain with highly conductive thin boundary. We obtain those results for matrix-valued conductivities and a family of speed measures (measures of the underlying domain). In particular, this family includes the Lebesgue measure and the one which makes the energy functional superposition. The expectation of the displacement of the associated processes close to the boundary goes to +∞ due to the explosion of the conductivity at the limit.
AB - The Mosco-convergence of energy functionals and the convergence of associated Wiener measures are proved for a domain with highly conductive thin boundary. We obtain those results for matrix-valued conductivities and a family of speed measures (measures of the underlying domain). In particular, this family includes the Lebesgue measure and the one which makes the energy functional superposition. The expectation of the displacement of the associated processes close to the boundary goes to +∞ due to the explosion of the conductivity at the limit.
KW - Mosco-convergence
KW - Singular homogenization
KW - Singular perturbation
KW - Tightness
KW - Weighted elliptic operators
KW - Wiener measures
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U2 - 10.1016/j.jmaa.2011.06.004
DO - 10.1016/j.jmaa.2011.06.004
M3 - Article
AN - SCOPUS:79961027005
SN - 0022-247X
VL - 384
SP - 504
EP - 526
JO - Journal of Mathematical Analysis and Applications
JF - Journal of Mathematical Analysis and Applications
IS - 2
ER -