Bi-H(o|¨)lder Mappings And Integrability For Solutions To Anisotropic Obstacle Problems

There are two topics in this paper. The first one is about the bi-Holder mappings. In this section, I will give the definition of the bi-Holder mappings firstly, which generalizes the concept of bi-Lipschitz mappings, then some properties of bi-Holder mappings are obtained. The second topic is about the integrability for solutions to κφ,θ(pi)-obstacle problems of the nonhomogeneous anisotropic elliptic equations. In2012, F.Leonetti and F.Siepe [10] considered solutions to boundary value problems of some anisotropic elliptic equations of the type Under some suitable conditions, they obtained an integrability result, which shows that, higher integrability of the boundary datum θ forces solutions u to have higher integra-bility as well. In the present paper, we consider κφ,θ(pi)-obstacle problems of the nonho-mogeneous anisotropic elliptic equations Under some controllable growth and monotonicity conditions. We obtain an integrability result, which can be regarded as a generalization of the result due to Leonetti and Siepe.