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In this paper, we study the partial regularity properties of vector valued functions u minimizing certain quadratic functionals with an unbounded obstacle which is defined by.

We prove existence and partial regularity of minimizers of certain functionals in the calculus of variations, under the main assumption that integrands be quasiconvex, and introduce a definition of general-quasiminima (G - Qminima), and prove some regularity results in Lpfor G - Qminima as well as for Q-minima.

Abstract: Suppose thatM is a complete Riemannian manifolds with nonnegative sectional curvature. We prove that any bounded exponentially harmonic function onM is a constant function.