Partial Differential Equations

analytic function arbitrary boundary data boundary value problem caso Cauchy data Cauchy problem characteristic curves characteristic equation characteristic strips coefficients completes the proof consider considor const continuous function continuous in D+ continuous second converge curvo defined depondent derivativos Dirichlet problem domain dorivatives dxdy easily verified follows formula fundamental solution given givon Green's function Green's identity harmonic function havo heat equation hence honco initial conditions initial curve initial data initial manifold initial value problem integral equation integral surface neighborhood non-characteristic obtain oquation order derivatives order equation ordinary differential equations ordor oxists P₁ power series quantity quasi-linear Riemann function satisfy second order solve suppose tangent theorem tho boundary tho function tho initial Thon thoorom u₁ un+1 uniformly unique valuo vanish variables whore