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To the problem of passage to the limit in divergent nonuniformly elliptic equations. (English. Russian original) Zbl 1085.35054

Funct. Anal. Appl. 35, No. 1, 19-33 (2001); translation from Funkts. Anal. Prilozh. 35, No. 1, 23-39 (2001).
Summary: 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.

MSC:

35J20 Variational methods for second-order elliptic equations
35J05 Laplace operator, Helmholtz equation (reduced wave equation), Poisson equation
46E35 Sobolev spaces and other spaces of “smooth” functions, embedding theorems, trace theorems
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