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  1. Calculus of Variations and Partial Differential Equations
  2. Calculus of Variations and Partial Differential Equations : Volume 37
  3. Calculus of Variations and Partial Differential Equations : Volume 37, Issue 3-4, March 2010
  4. The quasiconvex hull for the five-gradient problem
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Calculus of Variations and Partial Differential Equations : Volume 56
Calculus of Variations and Partial Differential Equations : Volume 55
Calculus of Variations and Partial Differential Equations : Volume 54
Calculus of Variations and Partial Differential Equations : Volume 53
Calculus of Variations and Partial Differential Equations : Volume 52
Calculus of Variations and Partial Differential Equations : Volume 51
Calculus of Variations and Partial Differential Equations : Volume 50
Calculus of Variations and Partial Differential Equations : Volume 49
Calculus of Variations and Partial Differential Equations : Volume 48
Calculus of Variations and Partial Differential Equations : Volume 47
Calculus of Variations and Partial Differential Equations : Volume 46
Calculus of Variations and Partial Differential Equations : Volume 45
Calculus of Variations and Partial Differential Equations : Volume 44
Calculus of Variations and Partial Differential Equations : Volume 43
Calculus of Variations and Partial Differential Equations : Volume 42
Calculus of Variations and Partial Differential Equations : Volume 41
Calculus of Variations and Partial Differential Equations : Volume 40
Calculus of Variations and Partial Differential Equations : Volume 39
Calculus of Variations and Partial Differential Equations : Volume 38
Calculus of Variations and Partial Differential Equations : Volume 37
Calculus of Variations and Partial Differential Equations : Volume 37, Issue 3-4, March 2010
The Willmore boundary problem
Solutions of Aronsson equation near isolated points
New extremal domains for the first eigenvalue of the Laplacian in flat tori
A Liouville theorem, a-priori bounds, and bifurcating branches of positive solutions for a nonlinear elliptic system
Semilinear elliptic equations with singular nonlinearities
An easy proof of Jensen’s theorem on the uniqueness of infinity harmonic functions
Curvature estimates for submanifolds with prescribed Gauss image and mean curvature
Everywhere regularity of certain nonlinear diffusion systems
Infinitely many positive solutions for the nonlinear Schrödinger equations in $${\mathbb{R}^N}$$
Non existence of quasi-harmonic spheres
The quasiconvex hull for the five-gradient problem
Relative minimizers of energy are relative minimizers of area
A class of integral equations and approximation of p-Laplace equations
Lack of coercivity in a concave–convex type equation
Erratum to: Fractures and vector valued maps
Calculus of Variations and Partial Differential Equations : Volume 37, Issue 1-2, January 2010
Calculus of Variations and Partial Differential Equations : Volume 36
Calculus of Variations and Partial Differential Equations : Volume 35
Calculus of Variations and Partial Differential Equations : Volume 34
Calculus of Variations and Partial Differential Equations : Volume 33
Calculus of Variations and Partial Differential Equations : Volume 32
Calculus of Variations and Partial Differential Equations : Volume 31
Calculus of Variations and Partial Differential Equations : Volume 30
Calculus of Variations and Partial Differential Equations : Volume 29
Calculus of Variations and Partial Differential Equations : Volume 28
Calculus of Variations and Partial Differential Equations : Volume 27
Calculus of Variations and Partial Differential Equations : Volume 26
Calculus of Variations and Partial Differential Equations : Volume 25
Calculus of Variations and Partial Differential Equations : Volume 24
Calculus of Variations and Partial Differential Equations : Volume 23
Calculus of Variations and Partial Differential Equations : Volume 22
Calculus of Variations and Partial Differential Equations : Volume 21
Calculus of Variations and Partial Differential Equations : Volume 20
Calculus of Variations and Partial Differential Equations : Volume 19
Calculus of Variations and Partial Differential Equations : Volume 18
Calculus of Variations and Partial Differential Equations : Volume 17
Calculus of Variations and Partial Differential Equations : Volume 16
Calculus of Variations and Partial Differential Equations : Volume 15
Calculus of Variations and Partial Differential Equations : Volume 14
Calculus of Variations and Partial Differential Equations : Volume 13
Calculus of Variations and Partial Differential Equations : Volume 12
Calculus of Variations and Partial Differential Equations : Volume 11
Calculus of Variations and Partial Differential Equations : Volume 10
Calculus of Variations and Partial Differential Equations : Volume 9
Calculus of Variations and Partial Differential Equations : Volume 8
Calculus of Variations and Partial Differential Equations : Volume 7
Calculus of Variations and Partial Differential Equations : Volume 6
Calculus of Variations and Partial Differential Equations : Volume 5

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The quasiconvex hull for the five-gradient problem

Content Provider SpringerLink
Author Pompe, Waldemar
Copyright Year 2009
Abstract In [8 Chapter 4.3] Kirchheim and Preiss gave an example of a set K consisting of five 2 × 2 symmetric matrices without rank-one connections, for which there exists a Lipschitz mapping u satisfying $${Du \in K}$$ . In the present paper we construct the rank-one convex hull of K. As a corollary we obtain that for each $${F \in {\rm int}\,K^{rc}}$$ there exists a Lipschitz mapping u satisfying $$Du \in K\quad{\rm and}\quad u(x) = Fx\,{\rm for}\,x\,\in\,{\partial} \Omega \,.$$ Moreover, we show that the rank-one convex hull of K and the quasiconvex hull of K are equal.
Ending Page 473
Page Count 13
Starting Page 461
File Format PDF
ISSN 09442669
e-ISSN 14320835
Journal Calculus of Variations and Partial Differential Equations
Issue Number 3-4
Volume Number 37
Language English
Publisher Springer-Verlag
Publisher Date 2009-09-11
Publisher Place Berlin, Heidelberg
Access Restriction One Nation One Subscription (ONOS)
Subject Keyword Calculus of Variations and Optimal Control; Optimization Systems Theory, Control Convexity, generalizations Theoretical, Mathematical and Computational Physics Analysis Problems involving relations other than differential equations
Content Type Text
Resource Type Article
Subject Applied Mathematics Analysis
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