Generalized Analytic Functions

By Friedrich Sauvigny. 2012

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The Calderón problem with partial data in two dimensions (2010, background): “Here we note that we can represent ek+iẽk = z′(s)χk(z(s)) (Section 2 of Chapter IV of [32]) where s is the length parameter of Γ̃ from one fixed point on Γ̃, z(s) is the parametrization of Γ̃, and χk(z) are some real-valued functions.”
The Beltrami equations and prime ends (2015, background): “, §6 of Chapter 4 in [52], the Dirichlet problem for the Beltrami equations, generally speaking, has no regular solution in the class of functions continuous (single-valued) in C with generalized derivatives in the case of multiply connected domains D.”
Differential Geometry of Special Mappings (2019, background): “3.1 Riemannian manifolds Vn, i.e. Riemannian and pseudo-Riemannian manifolds .”
Partial Cauchy data for general second order elliptic operators in two dimensions (2010, unknown): “Here ψ∗ k is a smooth function such that ψ ∗ k |Γ0 = 0 and the pair (L(φ̂ k , ψ̂ k), ψ∗ k) is orthogonal to all solutions of the adjoint problem (see [21]).”