Abstract

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 μ\mu in a particular class of continuous functions, that there is a variational integral and boundary conditions such that, for every p from [1,∞][1,\infty], the infimum is equal to μ(p)\mu(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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Contact details are reproduced from the original publication and may be historical.

M. Foss

Kansas State University, Dept. of Mathematics, Manhattan, KS 66506-2602, U.S.A.

foss@math.ksu.edu

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Suggested citation

M. Foss. “Examples of the Lavrentiev Phenomenon with Continuous Sobolev Exponent Dependence.” Journal of Convex Analysis 10 (2003), No. 2, 445–464. https://doi.org/10.68381/jca1027

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Published by Heldermann Verlag, 2003. Rights now held by Banach Press.