The Weak Repulsion Property
نویسنده
چکیده
In 1926 M. Lavrentiev [7] proposed an example of a variational problem whose infimum over the Sobolev spaceW, for some values of p ≥ 1, is strictly lower than the infimum overW1,∞. This energy gap is known since then as the Lavrentiev phenomenon. The aim of this paper is to provide a deeper insight into this phenomenon by shedding light on an unnoticed feature. Any energy that presents the Lavrentiev gap phenomenon is unbounded in any neighbourhood of any minimizer in W. We also show a finer result in case of regular minimizers and the repulsion property (observed by J. Ball and V. Mizel [3]) for any power α > 1 of a Lagrangian that exhibits the Lavrentiev gap phenomenon.
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تاریخ انتشار 2007