Lectures on Partial and Pfaffian Differential Equations |
Contents
1 | 10 |
SecondOrder Differential Equations and Integral Relations | 17 |
4 | 26 |
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1st kind arbitrary assume boundary condition boundary vector-family Cauchy problem characteristic coefficients const constant continuous solution continuously differentiable d„G¹ d₂u determine domain double integral dx¹ dx² dx³ existence theorem exterior derivative exterior product follows formula Green's formula Green's function Green's theorem Hence Hölder-continuous holds homogeneous boundary-value problem hyperbolic initial curve initial values initial-value problem integral equation integral manifold integral relation Lemma line-integral linear linearly independent maximum principle normal form obtain P₁ parabolic partial differential equation Pfaffian forms prescribed quadratic form right-hand member satisfies Section 4.4 singular tion transformation U₁ U₂ uniquely vanish variables vector w₁ w₂ zeros ஞ்