Quasiconvex functions and nonlinear PDEs
نویسندگان
چکیده
منابع مشابه
Quasiconvex Functions and Nonlinear Pdes
A second order characterization of functions which have convex level sets (quasiconvex functions) results in the operator L0(Du,Du) = min{v ·D2u vT | |v| = 1, |v ·Du| = 0}. In two dimensions this is the mean curvature operator, and in any dimension L0(Du,Du)/|Du| is the first principal curvature of the surface S = u−1(c). Our main results include a comparison principle for L0(Du,Du) = g when g ...
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In this note we construct new examples of quasiconvex functions defined on the set Sn×n of symmetric matrices. They are built on the k-th elementary symmetric function of the eigenvalues, k = 1, 2, ..., n. The idea is motivated by Šverák’s paper [S]. The proof of our result relies on the theory of the so-called k-Hessian equations, which have been intensively studied recently, see [CNS], [T], [...
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We give several examples of modeling in nonlinear elasticity where a quasiconvexification procedure is needed. We first recall that the three-dimensional Saint Venant-Kirchhoff energy fails to be quasiconvex and that its quasiconvex envelope can be obtained by means of careful computations. Second, we turn to the mathematical derivation of slender structure models: an asymptotic procedure using...
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This class of functions strictly contains the class of convex functions defined on a convex set in a real linear space. See [8] and citations therein for an overview of this issue. Some recent studies have shown that quasiconvex functions have quite close resemblances to convex functions – see, for example, [4], [6], [7], [10] for quasiconvex and even more general extensions of convex functions...
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ژورنال
عنوان ژورنال: Transactions of the American Mathematical Society
سال: 2013
ISSN: 0002-9947,1088-6850
DOI: 10.1090/s0002-9947-2013-05760-1