Lectures on Cauchy's Problem in Linear Partial Differential Equations

adjoint admit analytic function arbitrary assumed Book boundary calculation Calculus of Variations Cauchy Cauchy's problem characteristic cone characteristic conoid coefficients considered const constant convergence coordinates corresponding curvilinear coordinates cylinder Darboux deduced defined denoting derivatives determinate domain double integral duly inclined dv dv dx₁ element elementary solution equal exist expansion expression factor finite formula geodesic given gives Green's formula half conoid holomorphic function improper integral independent variables infinitesimal inside instance integration with respect Jacobian latter Leçons linear m₁ method neighbourhood obtained ordinary ordinary differential equations parameters partial differential equation plane polynomial positive quantity regular replaced result right-hand side satisfy simple integral singular space surface tangent term theorem transversal u₁ U₂ vertex Volterra's ди ду дх