TY - JOUR

T1 - On Derivation of Euler-Lagrange Equations for incompressible energy-minimizers

AU - Karakhanyan, Aram

AU - Chaudhuri, Nirmalendu

PY - 2009/12

Y1 - 2009/12

N2 - We prove that any distribution q satisfying the grad-div system q=divf for some tensor f=(fji)fjihr(U)(1r) -the local Hardy space; q is in h r and q is locally represented by the sum of singular integrals of fji 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 u2cofu2h1 . We also derive the system of Euler–Lagrange equations for volume preserving local minimizers u that are in the space Kloc13 [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.

AB - We prove that any distribution q satisfying the grad-div system q=divf for some tensor f=(fji)fjihr(U)(1r) -the local Hardy space; q is in h r and q is locally represented by the sum of singular integrals of fji 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 u2cofu2h1 . We also derive the system of Euler–Lagrange equations for volume preserving local minimizers u that are in the space Kloc13 [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.

UR - http://www.scopus.com/inward/record.url?scp=70449519435&partnerID=8YFLogxK

U2 - 10.1007/s00526-009-0248-z

DO - 10.1007/s00526-009-0248-z

M3 - Article

SN - 1432-0835

VL - 36

SP - 627

EP - 645

JO - Calculus of Variations and Partial Differential Equations

JF - Calculus of Variations and Partial Differential Equations

IS - 4

ER -