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Journal of Convex Analysis 10 (2003), No. 2, 445--464
Copyright Heldermann Verlag 2003
Examples of the Lavrentiev Phenomenon with Continuous Sobolev Exponent Dependence
M. Foss
Kansas State University, Dept. of Mathematics, Manhattan, KS 66506-2602, U.S.A.,
foss@math.ksu.edu
We construct variational problems with infima that have non-trivial
continuous dependence upon the Sobolev space from which the competing
functions are taken. It is shown, for each m
in a particular class of continuous functions, that there is a variational
integral and boundary conditions such that, for every p from [1, infinity],
the infimum is equal to m(p) if the admissible
class is a subset of W1, p. Thus, the manner in which the
infimum depends upon the Sobolev exponent may be prescribed.
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