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We have decided to discontinue the publication of preprints on our preprint server end of 2024. The publication culture within mathematics has changed so much due to the rise of repositories such as ArXiV (www.arxiv.org) that we are encouraging all institute members to make their preprints available there. An institute's repository in its previous form is, therefore, unnecessary. The preprints published to date will remain available here, but we will not add any new preprints here.
Relaxation of three solenoidal wells and characterization of three-phase
Mariapia Palombaro and Valery P. Smyshlyaev
Abstract
We study the problem of characterizing quasiconvex hulls for three "solenoidal" (divergence free) wells in dimension three when the wells are pairwise incompatible. A full characterization is achieved by combining certain ideas based on Šverák's example of a "nontrivial" quasiconvex function and on Müller's wavelet expansions estimates in terms of the Riesz transform. As a by-product, we obtain a new more general "geometrical" result: characterization of extremal three-point
- Received:
- 19.12.07
- Published:
- 19.12.07
- MSC Codes:
- 34A60, 49J45
- Keywords:
- differential inclusions, relaxation, $H$-measures and their characterization, Three-well problem, quasiconvex hulls, H-measures and their characterization