Holder Estimates for Higher Dimensional Corner Models

This chapter establishes Hölder space estimates for higher dimensional corner model problems. It first explains the homogeneous Cauchy problem before estimating the solution of the inhomogeneous problem in a n-dimensional corner. It then reduces the proof of an estimate in higher dimensions to the estimation of a product of 1-dimensional integrals. Using the “1-variable-at-a-time” method, the chapter proves the higher dimensional estimates in several stages by considering the “pure corner” case where m = 0, and then turns to the Euclidean case, where n = 0. It also discusses the resolvent operator as the Laplace transform of the heat kernel.