Mathematik in den Naturwissenschaften Leipzig Relaxation of three solenoidal wells and characterization of three - phase H - measures
نویسندگان
چکیده
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 H-measures for three-phase mixtures in dimension three. We also discuss the applicability of the latter result to problems with other kinematic constrains, in particular to that of three linear elastic wells.
منابع مشابه
Relaxation of three solenoidal wells and characterization of three phase H-measures
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 for a generic regime is achieved by translating the problem into the language of H-measures, following recipes of Kohn and Smyshlyaev & Willis, in combination with certain ideas based on Šverák’s example of a...
متن کاملRelaxation of Three Solenoidal Wells and Characterization of Extremal Three-phase H-measures
We fully characterize quasiconvex hulls for three arbitrary solenoidal (divergence free) wells in dimension three. With this aim we establish weak lower semicontinuity of certain functionals with integrands restricted to generic twodimensional planes and convex in (up to three) rank-2 directions within the planes. Within the framework of the theory of compensated compactness, the latter represe...
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