On Singular Solutions of Nonlinear Elliptic and Parabolic Equations

This lecture presents some results by L. Caffarelli, Y.Y. Li, and the speaker, from [2], [3] and [4]. They concern extensions to singular solutions of various forms of the maximum principle; they consist of some small technical results.     

Local boundary regularity of holomorphic mappings

Let f be a holomorphic mapping between two bounded domains D and D' in complex space ?ⁿ. Suppose that D and D' contain smooth real hypersurfaces Γ and Γ′ as open subsets of their respective boundaries, which correspond under a continuous extension of f. We shall show that this extension is smooth, given certain restrictions on Γ, Γ, and f.