Asymptotic behaviour and correctors for linear Dirichlet problems with simultaneously varying operators and domains
By Gianni Dal Maso, François Murat. 2002
47 citations recorded by the source corpus.
Abstract We consider a sequence of Dirichlet problems in varying domains (or, more generally, of relaxed Dirichlet problems involving measures in M 0 + (Ω) ) for second order linear elliptic operators in divergence form with varying matrices of coefficients. When the matrices H-converge to a matrix A0, we prove that there exist a subsequence and a measure μ0 in M 0 + (Ω) such that the limit problem is the relaxed Dirichlet problem corresponding to A0 and μ0. We also prove a corrector result which provides an explicit approximation of the solutions in the H1-norm, and which is obtained by multiplying the corrector for the H-converging matrices by some special test function which depends both on the varying matrices and on the varying domains.
Subfields: Applied Mathematics, Computational Mechanics, Computational Theory and Mathematics
View Paper: https://www.semanticscholar.org/paper/0e60bba68ee9e4b69ca05fb8a47dce165d555565
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In Applied Mathematics
In Computational Mechanics
In Computational Theory and Mathematics
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Citations in the corpus
- A semilinear elliptic equation with a mild singularity at $u=0$: existence and homogenization (2015, background): “It is then (well) known (1) (see e.g. [7] Section 1 and [8] Section 2.2 for more details) that if z ∈ H 10 (Ω), then z (or more exactly its quasi-continuous representative for the H 10 (Ω) capacity) satisfies When one assumes that the holes , are such that the assumptions (5.1), (5.2), (5.3), (5.4),…”
- Asymptotic behavior of the solutions of a nonlinear Robin problem for the Laplace operator in a domain with a small hole: a functional analytic approach (2007, background): “9 , and the vast literature of homogenization theory (cf Dal Maso and Murat 10 ).”
- Asymptotic analysis of periodically-perforated nonlinear media (2002, methodology): “... of functions (u‐), converging to a function u, which equal the constant u(x‐i) on suitable annuli surrounding B‐ i . The contribution of these functions on such annuli easily leads to the formula defining ’. This method seems of interest also since it can be easily applied to sequences of integr”