Interpolation inequalities in pattern formation
DOI:
https://doi.org/10.6092/issn.2240-2829/2666Abstract
In this seminar I will present some interpolation inequalities that involves the BV-norm and some negative norms of a function u. These inequalities are the strong version of some already known estimates in weak form, which play a crucial role in the study of pattern formation. The main ingredient in the proof of these estimates is given by a geometric construction, that was first used by Choksi, Conti, Kohn and Otto in the context of branched patterns in superconductors, and which main idea goes back to De Giorgi. This is a joint work with Felix Otto.
References
R. Choksy, S. Conti, R. Kohn, and F. Otto, Ground state energy scaling laws during the onset and destruction of the intermediate state in a type I superconductor, Comm. Pure Appl. Math, 61(5) (2008), 595-626.
A. Cohen, W. Dahmen, I. Daubechies, and R. DeVore, Harmonic analysis of the space BV, Rev. Mat. Iberoamericana, 19(1) (2003), 235{263.
S. Conti, B. Niethammer, and F. Otto, Coarsening rates in ocritical mixture, SIAM J. Math. Anal., 37(6) (2006), 1732-1741.
R. Kohn and F. Otto, Upper bounds on coarsening rates, Comm. Math. Phys., 229(3) (2002), 375-395.
M. Ledoux, On improved Sobolev embedding theorems, Mathematical Research Letters 10 (2003), 659-669.
F. Otto, T. Rump, and D. Slepcev, Coarsening rates for a droplet model: rigorous upper bounds, SIAM J. Math. Anal., 38(2) (2006), 503-529.
T. Viehmann, Uniaxial Ferromagnets, Doctoral Thesis, University of Bonn (2009).
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