INTEGRAIS COMPLEXAS E DE SUPERFÍCIES DE ANCELMO L. GRACELI [16]

EQUAÇÕES MULTIDIMENSIONAL DE ANCELMO L. GRACELI

$\Delta \varphi =f$ = $\nabla ^{2}$ = Φ x s / $\partial D$ + Φ ys / $\partial D$ + Φ z / $\partial D$ + Φ w S / $\partial D$ [n] dD............

$\Delta \varphi =f$ = $\nabla ^{2}$ = Φ x S/ $\partial D$ + Φ y S / $\partial D$ + Φ zS / $\partial D$ + Φ wS / $\partial D$ [n].dD [n]...............

$\Delta \varphi =f$ = $\nabla ^{2}$ = $\varphi$ Φ x / $\partial D$ + $\varphi$ Φ y / $\partial D$ + $\varphi$ Φ z / $\partial D$ + $\varphi$ Φ w/ $\partial D$ [n]. dD...........

$\Delta \varphi =f$ = $\nabla ^{2}$ = $\varphi$ S S $\varphi$ Φ x / $\partial D$ +S $\varphi$ Φ y / $\partial D$ + S $\varphi$ Φ z / $\partial D$ + $\varphi$ Φ w/ $\partial D$ [n] .dΦ dD [n]...............

EQUAÇÕES MULTIDIMENSIONAL DE ANCELMO L. GRACELI

$\Delta \varphi =f$ = $\nabla ^{2}$ = Φ x / $\partial D$ + Φ y / $\partial D$ + Φ z / $\partial D$ + Φ w/ $\partial D$ [n]............

$\Delta \varphi =f$ = $\nabla ^{2}$ = Φ x / $\partial D$ + Φ y / $\partial D$ + Φ z / $\partial D$ + Φ w/ $\partial D$ [n].dΦ [n]...............

EQUAÇÕES MULTIDIMENSIONAL DE ANCELMO L. GRACELI

$\Delta \varphi =f$ = $\nabla ^{2}$ = Φ x / $\partial D$ + Φ y / $\partial D$ + Φ z / $\partial D$ + Φ w/ $\partial D$ [n]............

$\Delta \varphi =f$ = $\nabla ^{2}$ = Φ x / $\partial D$ + Φ y / $\partial D$ + Φ z / $\partial D$ + Φ w/ $\partial D$ [n].dΦ [n]...............

$\Delta \varphi =f$ = $\nabla ^{2}$ = $\varphi$ Φ x / $\partial D$ + $\varphi$ Φ y / $\partial D$ + $\varphi$ Φ z / $\partial D$ + $\varphi$ Φ w/ $\partial D$ [n]............

$\Delta \varphi =f$ = $\nabla ^{2}$ = S $\varphi$ S $\varphi$ Φ x / $\partial D$ +S $\varphi$ Φ y / $\partial D$ + S $\varphi$ Φ z / $\partial D$ + S $\varphi$ Φ w/ $\partial D$ [n] .dΦ [n]...............

EQUAÇÕES MULTIDIMENSIONAL DE ANCELMO L. GRACELI

$\nabla ^{2}$ $\phi (x)$ = Φ x / $\partial D$ + Φ y / $\partial D$ + Φ z / $\partial D$ + Φ w/ $\partial D$ [n]............

$\nabla ^{2}$ $\phi (x)$ = Φ x / $\partial D$ + Φ y / $\partial D$ + Φ z / $\partial D$ + Φ w/ $\partial D$ [n].dΦ [n]...............

$\nabla ^{2}$ $\phi (x)$ = $\varphi$ Φ x / $\partial D$ + $\varphi$ Φ y / $\partial D$ + $\varphi$ Φ z / $\partial D$ + $\varphi$ Φ w/ $\partial D$ [n]............

$\nabla ^{2}$ $\phi (x)$ = $\varphi$ Φ x / $\partial D$ + $\varphi$ Φ y / $\partial D$ + $\varphi$ Φ z / $\partial D$ + $\varphi$ Φ w/ $\partial D$ [n] .dΦ [n]...............

EQUAÇÕES MULTIDIMENSIONAL DE ANCELMO L. GRACELI

$\Psi _{n}$ $\phi (x)$ = Φ x / $\partial D$ + Φ y / $\partial D$ + Φ z / $\partial D$ + Φ w/ $\partial D$ [n]............

$\Psi _{n}$ $\phi (x)$ S = S Φ x / $\partial D$ +S Φ y / $\partial D$ + S Φ z / $\partial D$ + S Φ w/ $\partial D$ [n].dΦ dD [n]...............

$\Psi _{n}$ $\phi (x)$ = $\varphi$ Φ x / $\partial D$ + $\varphi$ Φ y / $\partial D$ + $\varphi$ Φ z / $\partial D$ + $\varphi$ Φ w/ $\partial D$ [n]............

$\Psi _{n}$ $\phi (x)$ = S S $\varphi$ Φ x / $\partial D$ +S $\varphi$ Φ y / $\partial D$ + S $\varphi$ Φ z / $\partial D$ + S $\varphi$ Φ w/ $\partial D$ [n] .dΦ [n]...............

Condição de contorno de Dirichlet

Diz que a equação de Poisson tem condições de contorno de Dirichlet quando a função incógnita $\varphi$ é explicitamente descrita no contorno do domínio, i.e.:

domínio $D$ tendo um contorno suficientemente suave $\partial D$ ,

o operador laplaciano é denotado por $\nabla ^{2}$ . Esta notação é motivada pelo fato de que $\Delta =\nabla \cdot \nabla$ , onde $\nabla$ denota o gradiente. Quando $f\equiv 0$ a equação é chamada de equação de Laplace.

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INTEGRAIS COMPLEXAS E DE SUPERFÍCIES DE ANCELMO L. GRACELI [16]

Condição de contorno de Dirichlet

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