NDLI: On derivation of Euler–Lagrange equations for incompressible energy-minimizers

Content Provider	SpringerLink
Author	Chaudhuri, Nirmalendu Karakhanyan, Aram L.
Copyright Year	2009
Abstract	We prove that any distribution q satisfying the grad-div system $${\nabla q={\rm div}\,{\bf f}}$$ for some tensor $${{\bf f}=(f^i_j), \,f^i_j\in h^r(U)\,(1\leq r < \infty}$$ ) -the local Hardy space; q is in h r and q is locally represented by the sum of singular integrals of $${f^i_j}$$ with Calderón-Zygmund kernel. As a consequence, we prove the existence and the local representation of the hydrostatic pressure p (modulo constant) associated with incompressible elastic energy-minimizing deformation u satisfying $${\|\nabla{\bf u}\|^2,\,\|{\rm cof}\,\nabla{\bf u}\|^2\in h^1}$$ . We also derive the system of Euler–Lagrange equations for volume preserving local minimizers u that are in the space $${K^{1,3}_{\rm loc}}$$ [defined in (1.2)]—partially resolving a long standing problem. In two dimensions we prove partial C 1,α regularity of weak solutions provided their gradient is in L 3 and p is Hölder continuous.
Ending Page	645
Page Count	19
Starting Page	627
File Format	PDF
ISSN	09442669
e-ISSN	14320835
Journal	Calculus of Variations and Partial Differential Equations
Issue Number	4
Volume Number	36
Language	English
Publisher	Springer-Verlag
Publisher Date	2009-06-03
Publisher Place	Berlin, Heidelberg
Access Restriction	One Nation One Subscription (ONOS)
Subject Keyword	Calculus of Variations and Optimal Control; Optimization Systems Theory, Control Theoretical, Mathematical and Computational Physics Analysis Nonlinear elliptic equations
Content Type	Text
Resource Type	Article
Subject	Applied Mathematics Analysis

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