Regularity For Minimizing Sequences Of Some Integral Functionals

This paper deals with regularity properties for minimizing sequences of some integral func-tionals related to nonlinear elasticity theory.Let ?(?)R3 be a bounded open subset.We deal with integral functionals J(u)=??f(x,Du(x))dx defined on vector valued mappings u=(u1,u2,u3)t:?(?)R3?R3,where f(x,Du):Q�R3�3?R is a Caratheodory function.We consider two special classes of integrands:f(x,Du)=F(x,Du)+G(x,adj2Du)+H(x,det Du)(*)and f(x,Du)=(?)F?(x,Du?)+G(x,adj2Du)+H(x,det Du),here Du is the 3 � 3 Jacobi matrix of the partial derivatives for u,adj2 Du=((adj2Du)i?)?R3�3 denotes the adjugate matrix of order 2,?,i?{1,2,3},det Du is the determinant of the matrix Du.In nonlinear elasticity theory,?,adj2? and det? govern the deformations of line,surface and volume,respectively.Under some appropriate conditions on F,F?,G,H,we derive that the minimizing sequences and the gradients of the sequences have some regularity properties by using the Ekeland variational principle.The main feature of the present paper is that the integrand(*)is not of splitting form,and we use an alternative norm for a vector,which allows us to deal with the exponent p in the interval(1,3).