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- W1553665166 abstract "This paper discusses the relaxation of a multiwell energy of the special form W = mini{|▽u − ai|2}. We explain how the relaxation QW can be expressed in terms of certain “tensors of geometric parameters.” The exact set ℱθ of attainable geometric parameters is not known, but we show that it must lie inside an explicitly given convex set ℱ θ U . This leads to a new Geometric Parameters Lower Bound for QW. For the special case of threewells in two space dimensions we give a complete characterization of the extreme points of ℱ θ U . The final section addresses the “three gradient problem,” which asks whether three pairwise incompatible gradients can nevertheless be mutually compatible. We do not solve this problem, but we show that it is linked to the attainability of the type 3 extreme points of ℱ θ U ." @default.
- W1553665166 created "2016-06-24" @default.
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- W1553665166 date "1993-01-01" @default.
- W1553665166 modified "2023-09-25" @default.
- W1553665166 title "Geometric Parameters and the Relaxation of Multiwell Energies" @default.
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- W1553665166 doi "https://doi.org/10.1007/978-1-4613-8360-4_6" @default.
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