DOI: 10.68381/jca09002 ISSN: 0944-6532
Some New Results on the Convergence of Degenerate Elliptic and Parabolic Equations
Fabio Paronetto
We consider a sequence of matrices
a_h(x,t)
a
h
(
x
,
t
)
whose minimum eigenvalue is a positive function
\lambda_h(x)
λ
h
(
x
)
and the maximum one is
L\lambda_h(x)
L
λ
h
(
x
)
,
\lambda_h
λ
h
satisfying a uniform Muckenhoupt's condition. We study G-convergence of the sequence of linear parabolic operators in divergence form associated to these matrices and with coefficient
\lambda_h
λ
h
in front of the temporal derivative. When the matrices are depending only on the variable x we compare this result with the analogous results for the sequence of elliptic operators and the sequence of standard parabolic operators associated to the same sequence of matrices.