We prove Harnack's inequality for non-negative solutions of some degenerate elliptic operators in divergence form with the lower order term coefficients satisfying a Kato type contition.
We construct biharmonic non-harmonic maps between Riemannian manifolds and by first making the ansatz that be a harmonic map and then deforming the metric on by to render biharmonic, where is a smooth function with gradient of constant norm on and . We construct new examples of biharmonic non-harmonic maps, and we characterize the biharmonicity of some curves on Riemannian manifolds.
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