Abstract
A weighted Sobolev space is constructed in which smooth functions are not dense and their closure is of codimension one. With the help of this weighted space, counterexamples are constructed to natural hypotheses on the passage to the limit in non-uniformly-elliptic equations and on the structure of the limit equation.
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Zhikov, V.V. To the Problem of Passage to the Limit in Divergent Nonuniformly Elliptic Equations. Functional Analysis and Its Applications 35, 19–33 (2001). https://doi.org/10.1023/A:1004168415999
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DOI: https://doi.org/10.1023/A:1004168415999