Weak lower semicontinuity of variational functionals with variable growth

Abstract

Abstract In this paper, we establish the weak lower semicontinuity of variational functionals with variable growth in variable exponent Sobolev spaces. The weak lower semicontinuity is interesting by itself and can be applied to obtain the existence of an equilibrium solution in nonlinear elasticity. 2000 Mathematics Subject Classification: 49A45

Keywords

• lower semicontinuity
• variational functional
• variable growth