Partial Differential EquationsNew York University, 1952 - 211 páginas |
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... continuous in D + B. Then it is clear that u must have a maximum ( minimum ) somewhero in D + B , since a continuous function always has a maximum ( minimum ) on a closed and bounded sot . From the previous thoorom wo know that this ...
... continuous in D + B. Then it is clear that u must have a maximum ( minimum ) somewhero in D + B , since a continuous function always has a maximum ( minimum ) on a closed and bounded sot . From the previous thoorom wo know that this ...
Página 124
... function u . b ) That u is continuous in D + B follows from the fact that a uniformly convergont soquonce of continuous functions convergo to a continuous function . To show that u is harmonic in D , or equivalently that u has the moan ...
... function u . b ) That u is continuous in D + B follows from the fact that a uniformly convergont soquonce of continuous functions convergo to a continuous function . To show that u is harmonic in D , or equivalently that u has the moan ...
Página 135
Fritz John. ၂ ။ Lemma 4. For fixed p , the cru continuous functions of ( 5 , in cvory closed subsot of D , whoro definod , and convorgo uniformly in E , to a continuous function ( 5 , np ) as 11 → ∞ . n Proof : It is clear that tho ...
Fritz John. ၂ ။ Lemma 4. For fixed p , the cru continuous functions of ( 5 , in cvory closed subsot of D , whoro definod , and convorgo uniformly in E , to a continuous function ( 5 , np ) as 11 → ∞ . n Proof : It is clear that tho ...
Contenido
Introduction | 1 |
THE CAUCHY PROBLEM FOR HIGHER ORDER EQUATIONS | 48 |
The Cauchy problem for the general nonlinear | 70 |
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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