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Classification of Secondorder Partial Differential Equa
Classification of Secondorder Equations in n Independ
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analogous analytic arbitrary assume axis bn(x boundary conditions bounded Cauchy problem Chapter characteristic closed region coefficients condition 8u Consider const continuous derivatives converges corresponding cosh curve cylinder defined degeneration denote density differential equation differential operator Dirichlet problem double layer eigenfunctions eigenvalues elliptic equation equation 82u exists finite formula Frankl fundamental solution given Green's formula Green's function half-plane harmonic function harmonic polynomials Holder condition hyperbolic equation independent variables inequality initial conditions integral equations Laplace operator Laplace's equation linear matrix method mixed boundary-value problems mixed problem Neumann problem nonhomogeneous norm normal obtain point Mo Poisson's equation polynomials potential problem for Equation Second Boundary-value Problem second derivatives second-order simple layer singular sinh solution of Equation solved space sufficiently smooth Suppose surface theorems theory Third Boundary-value Problem Tricomi problem unique solution unknown function values vanish vector wave equation well-posed zero