背景 球内区域 Laplace方程的边值问题 0 x=f(2)
Associated Legendre Functions Spheroidal Harmonics Eigenproblem of Associated Legendre Eqns Orthogonality of Associated Legendre Ftns µ ¥S«Laplace§>¯K ∇2u = 0 u Σ = f(Σ) À½¥IX§I: u¥% ѽ)¯K3¥IXeäN/ª C. S. Wu 1lù ¥¼ê(n)
背景 球内区域 Laplace方程的边值问题 0 x=f(2) ρ选定球坐标系,坐标原点位于球心 写出定解问题在球坐标系下的具体形式
Associated Legendre Functions Spheroidal Harmonics Eigenproblem of Associated Legendre Eqns Orthogonality of Associated Legendre Ftns µ ¥S«Laplace§>¯K ∇2u = 0 u Σ = f(Σ) À½¥IX§I: u¥% ѽ)¯K3¥IXeäN/ª C. S. Wu 1lù ¥¼ê(n)
背景 球内区域 Laplace方程的边值问题 0 x=f(2) ρ选定球坐标系,坐标原点位于球心 ●写出定解问题在球坐标系下的具体形式
Associated Legendre Functions Spheroidal Harmonics Eigenproblem of Associated Legendre Eqns Orthogonality of Associated Legendre Ftns µ ¥S«Laplace§>¯K ∇2u = 0 u Σ = f(Σ) À½¥IX§I: u¥% ѽ)¯K3¥IXeäN/ª C. S. Wu 1lù ¥¼ê(n)
背景 球内区域 Laplace方程的边值问题 V2u=0 u,=f(∑) 但在写出定解问题在球坐标系下的具体形式时,需要注意
Associated Legendre Functions Spheroidal Harmonics Eigenproblem of Associated Legendre Eqns Orthogonality of Associated Legendre Ftns µ ¥S«Laplace§>¯K ∇2u = 0 u Σ = f(Σ) 3ѽ)¯K3¥IXeäN/ª§I5¿ Laplace§3I:r = 0ؤá§3T: ¿Ùþ3u(r, θ, φ)érüýê rLaplace§U¥IX§ ± ½)¯K d5§ 7LÖ¿þu(r, θ, φ) 3I:r = 0?k.^ C. S. Wu 1lù ¥¼ê(n)
背景 球内区域 Laplace方程的边值问题 V2u=0 u,=f(∑) 但在写出定解问题在球坐标系下的具体形式时,需要注意 Laplace方程在坐标原点”=0不成立,在该点 充其量只存在(r,0,)对的单侧导数 把 Laplace方程改写到球坐标系时,为了保持 定解问题的等价性,还必须补充上(, 在坐标原点=0处的有界条件
Associated Legendre Functions Spheroidal Harmonics Eigenproblem of Associated Legendre Eqns Orthogonality of Associated Legendre Ftns µ ¥S«Laplace§>¯K ∇2u = 0 u Σ = f(Σ) 3ѽ)¯K3¥IXeäN/ª§I5¿ Laplace§3I:r = 0ؤá§3T: ¿Ùþ3u(r, θ, φ)érüýê rLaplace§U¥IX§ ± ½)¯K d5§ 7LÖ¿þu(r, θ, φ) 3I:r = 0?k.^ C. S. Wu 1lù ¥¼ê(n)