Methods of Mathematical Physics, Volume 2

analytic function assume boundary value problem bounded C₁ Cauchy data Cauchy's problem characteristic curves characteristic surfaces consider const construct continuously differentiable converges corresponding defined definition denote differential operator discontinuities domain G domain of dependence elliptic equa example exists expression formula func given Green's function hence Hölder Hölder condition Hölder continuous homogeneous hyperbolic ideal functions identically independent variables inequality initial conditions initial value problem integral surface interior manifold Math matrix mean value mean value theorem normal cone normal surface obtain ordinary differential equations parameter partial differential equation plane potential proof pseudoanalytic function quasi-linear ray cone relation respect satisfies second order singular solution solved space sphere tangent theorem theory tion transformation u₁ uniformly uniquely determined vanishes vector wave equation x-space zero