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Formulation of Boundary Value Problems in Mathematical Physics
Basic Equations of Mathematical Physics
Classification of Linear SecondOrder Differential Equations
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analogously arbitrary becomes zero boundary condition boundary value problem bounded Cauchy problem classical solution coefficients compact support continuous function converges uniformly convolution correct normal derivative defined denote density differential equation Dirichlet problem eigenfunctions eigenvalues exterior Dirichlet problem exterior Neumann problem fact Fourier transform Fredholm's theorems function u(x functions belonging fundamental solution grad Green's formula Green's function harmonic function Hilbert-Schmidt theorem inequality initial conditions integral equation interior Dirichlet Laplace's equation Lebesgue integrable lemma of Sec linear mixed problem neighborhood Neumann problem orthonormal perturbation point x0 polar kernel polynomial Proof region G respect right-hand side satisfies Eq side of Eq simple layer potential solubility solution of Eq solution u(x sphere spherical functions test functions theorem cf theorem is proved theorem of Sec tion unique valid variables virtue wave equation x e G y e G
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Nonlinear Functional Analysis and Its Applications: Part 2 B: Nonlinear ...
No preview available - 1989