
Journal of Convex Analysis 10 (2003), No. 2, 445464 Copyright Heldermann Verlag 2003 Examples of the Lavrentiev Phenomenon with Continuous Sobolev Exponent Dependence M. Foss Kansas State University, Dept. of Mathematics, Manhattan, KS 665062602, U.S.A., foss@math.ksu.edu We construct variational problems with infima that have nontrivial 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 W^{1, p}. Thus, the manner in which the infimum depends upon the Sobolev exponent may be prescribed. FullTextpdf (1.26 MB) 